Tuesday, November 29, 2016

find square roots of -1+2i

We have to find the square root of `-1+2i` i.e. `\sqrt{-1+2i}`


We will find the square roots of the complex number of the form x+yi , where x and y are real numbers, by the following method:


Let `z^2=(x+yi)^2=-1+2i`


i.e. `(x^2-y^2)+2xyi=-1+2i`


Comparing real and imaginary terms we get,


`x^2-y^2=-1 -------> (1)`


`2xy=2` implies `xy=1 ------>(2)`  


So from (2) we get,  y=1/x . Substituting this in (1) we have,


`x^2-\frac{1}{x^2}=-1`


i.e. `x^4+x^2-1=0`


implies `x^2=\frac{-1\pm\sqrt{5}}{2}`


               `=0.62, -1.62`


Therefore, `x=\pm\sqrt{0.62}=\pm 0.79` ``


`x^2=-1.62` is discarded since it gives imaginary value.


hence,


When x=0.79,  y= 1.27


         x=-0.79 , y= -1.27


i.e we have,  `\sqrt{-1+2i}=0.79+1.27i or -0.79-1.27i`


                                `=\pm (0.79+1.27i)`


Hence the square roots of -1+2i are:  `\pm` (0.79+1.27i)  

Monday, November 28, 2016

Why do people from different races look different?

Great question! Actually, it's not so much that people from different "races" look different, but that people who look different were categorized into races. I think it's really important for people to understand the historical and social context of the idea of race in order to fully make sense of how it impacts our lives today. Because I am most familiar with racial categories in the United States, I will use this as my central frame of reference. 


Race, as it is thought of in the Western world, describes categories of physical attributes like color of eyes, skin, and hair. In some parts of the world, race is quite different. Historically, Japan has been quite ethnically and phenotypically (the way people look) homogenous, so there wasn't really much of a concept of race until Europeans and Mainland Asians began to visit. In Brazil, racial categories are far more flexible and may take into account factors like socioeconomic status and who you hang out with-- not just appearance! Comparing understandings of race from around the world should tip us off to the fact that race is a cultural phenomenon rather than a physical one.


The truth is that there is no biological reality of race. There is no one gene, or even a collection of genes, which determine that a person is White or Black or Asian. Even trying to lump people into these categories leaves a lot out of the picture. Within one "racial category" and even within one nation or city, there's a lot of variation in how people look. Let's imagine you have a bag full of jellybeans of every possible flavor and color, and I asked you to sort them into distinct categories. You could try to sort them into categories like blue, red, green, and so on-- but what about the purple jellybeans, the light blue, or the red with orange spots? You'd probably do your best to sort these with the jellybeans they look most similar to, right? Our understanding of race is the same way-- we try to sort people into groups based on how they look in comparison with stereotypes of race.


Though race is not a biological reality in the sense that there is one gene or one phenotype for how people of a certain race look, our stereotypes of race are based on actual physical characteristics. Color of skin, hair, and eyes, facial bone structure, and the texture of hair all may play a part in how we intentionally or unintentionally categorize someone. That physical categorization on its own isn't necessarily a bad thing-- humans love to categorize things, even each other! When we treat these categorizations as being fixed realities, creating a sense of "either-or," it can cause a lot of conflict about physical appearance. Even worse, historically and to this day, many people assign value to certain characteristics or associate a physical appearance with social behavior.


This is why race is a damaging social construct. The idea of race and racial categories takes the full spectrum of human appearance, our mixed bag of jellybeans, and tries to push them into a handful of boxes that leave out a lot of information. Prior to European colonialism, the idea of race wasn't very fixed. In fact, prior to and during the 16th century, most people used the term "race" to refer to people of differing nationalities. With increasing exploration and colonization of the world, race came to refer to the many different ways people looked in addition to nationality. With the international slave trade, the idea that people from a particular place look a certain way transformed into a very rigid hierarchy of phenotype as justification for human cruelty.


In the 17th and 18th centuries, explorers and scientists tried to devise a system of neat categories of race. The most popular and persistent of these systems was that devised by John Friedman Blumenbach, who argued that there was a biologically real hierarchy of humans categorized as Caucasian, Mongoloid, Malay, Negroid, and (Indigenous) American. This hierarchy was primarily based on skin color, with the lightest (European) skin being favored, and the darkest (African) skin being considered lowest. Though it was outwardly based on appearance, this hierarchy took on all sorts of connotations of physical and mental capabilities. Much of the racial oppression and human injustice caused by the international slave trade was "justified" because light-skinned Europeans genuinely believed that people of darker skin tones were not as smart and possibly couldn't even feel pain. Some people went as far as believing that it was their duty as a light-skinned person to rule over, exploit, and "shepherd" darker-skinned people. 


As for why people from different parts of the world have different appearances, it's all about adaptation! Our species, Homo sapiens, first arose in Southeast Africa around 200,000 years ago. Since then, our ancestors have been busy spreading out around the globe. Though this journey was most likely motivated by a search for food, people eventually settled in every possible habitable environment. With exposure to these many variable environments, the general appearance of a population began to shift in response to environmental pressure. Our first Homo sapiens ancestors were likely dark-skinned, but those who migrated out of the high-sun environment of Sub-Saharan Africa did not require as much melanin to be present in the skin. Skeletal features like nose shape, height, or jaw shape may be a response to the air quality and diet of a particular region. 


Today, we know that the social connotations of race aren't true. Especially as genetic evidence expands, we know that there is no real, fixed, biological basis for racial identities. However, beliefs about race are so deeply ingrained in society that it takes active and critical thinking to undo the things we have been taught (implicitly and explicitly) about race. 

Sunday, November 27, 2016

What does Bryon mean when he says "that was then, this is now"?

In Chapter 4, Bryon and Mark are reminiscing about playing as children and getting into trouble with their friends when they were young. Mark then asks Bryon if he ever gets the feeling that things are coming to an end because something new is about to begin. Bryon tells Mark that he understands how he is feeling. Mark then mentions how they used to be very close with their other friends, but recently things have begun to change. They don't get to see their friends anymore because everyone is in a relationship or doing their own thing. Bryon agrees with Mark that things have changed and says that it is kind of a good thing. Mark then sighs and comments, "but there's a difference. I wonder what the difference is?" (Hinton 69). Bryon responds by saying,



"The difference is...that was then, this is now" (Hinton 69).



Bryon essentially means that as time progresses, people change and grow apart from one another. Bryon realizes that their childhood has come to an end and that the present stage of their lives is not the same as it once was. He is saying that the past is the past, and one must accept the ever-changing course of life.

Saturday, November 26, 2016

In Shakespeare's Macbeth, what are the obstacles to Lady Macbeth's plan?

One major obstacle to Lady Macbeth's plan is Macbeth himself.  She initially fears that he is "too full o' th' milk of human kindness" to consider killing the king in order to take the throne (1.5.17).  She turns out to be wrong -- he is willing to consider it -- but after Macbeth has had time to consider all the reasons he has not to kill Duncan, he tells her, "We will proceed no further in this business" (1.7.34).  Lady Macbeth must then convince him to overcome his scruples.


Lady Macbeth's own scruples and feelings present another obstacle to her plan.  She actually prays to be "unsex[ed]" because she wants to rid herself of any "remorse" she might have; likewise, she wishes to squash any compassion or womanly feelings that might prevent her from acting brutally (1.5.48, 1.5.51).  Then, when she goes to kill Duncan, she cannot.  Alone on stage, she says, "Had he not resembled / My father as he slept, I had done 't" (2.2.16-17).  So, it seems that Lady Macbeth is not quite as hard-hearted as she'd like to be, and her compassion -- however small -- presents another obstacle to her plan.

Thursday, November 24, 2016

What are the conflicts in the story "A & P" by John Updike?

There are three main conflicts in John Updike's "A & P": Man vs. Society, Man vs. Man, and Man vs. Self.


  • Man vs. Society

As Sammy, who narrates, checks out an older woman's groceries, he notices three girls who enter the store wearing "nothing but bathing suits." Because he becomes so distracted by these scantily-clad girls, Sammy rings up a box of HiHo crackers twice and the "witch about fifty with rouge on her cheekbones and no eyebrows" is able to catch him making an error. She complains to Sammy.
Further in the narrative, Sammy is critical of some of the customers, calling them names, such as "houseslaves in curlers." Then, he begins to feel defensive of the girls.


  • Man vs. Man 

Sammy comes into conflict with the store manager, Mr. Lengel, because he wants to defend the three girls that Lengel has accosted and told, "We want you decently dressed when you come in here." Lengel adds that they must have their shoulders covered, as it is "policy." 
All the time that Lengel talks with the girls, Sammy watches them until he becomes infatuated enough--"scrunchy inside"--to feel that he must defend them. He tells Mr. Lengel that he did not have to embarrass the girls, and in an act of bravado, he quits.



"Sammy, you don't want to do this to your Mom and Dad," he [Lengel] tells me. It's true, I don't. But it seems to me that once you begin a gesture it's fatal not to go through with it....


"You'll feel this for the rest of your life," Lengel says, and I know it's true.



  • Man vs. Self

Having acted against his better judgment, Sammy narrates that he keeps thinking of how Lengel made the pretty girl blush. After he has quit, Sammy searches for the girls, but they are gone. He looks through the window of the store, and realizes that he has defended the girls of his generation against the older generation only to find himself in some kind of limbo between the two. For, he does not know if he has acted as a fool or as a hero. Nevertheless, Sammy knows life will be harder: "I felt how hard the world was going to be to me hereafter."

What are examples of figurative language used in Act III, Scene 2 of King Lear?

Act III, Scene 2 of Shakespeare's King Lear is absolutely central to the play, and it accordingly employs some of the story's most lyrical language. The most extensive example of figurative language in this scene is personification, as Lear personifies the storm and raging elements by giving them human qualities. 


The first example of personification comes in the first line of the scene, when Lear urges the storm to "crack your cheeks; rage, blow" (1). The stormy elements of nature do not actually have cheeks, nor do they literally "rage." As such, we can see Lear is giving the elements human qualities and thus heightening our ability to imagine the intensity of the storm. Later in the scene, Lear advances his personification of the storm by calling the elements "servile ministers" (21), and so he directly imagines the storm having a human profession. 


It's also worth mentioning that this scene employs an apostrophe. In terms of figurative language, an apostrophe is an address to an absent character, or to a thing or abstract idea. In this scene, Lear very clearly addresses the storm as if it were a thinking being, saying "I tax not you, you elements, with unkindness" (16). Since the weather is not a thinking being or an actual character, Lear's direct address of the storm as "you" is an apostrophe.  

Wednesday, November 23, 2016

What are the names of important characters in Heidi by Johanna Spyri?

The protagonist is Heidi, a Swiss girl who lives with her aunt, Dete (also called "Detie"), in the mountains. Her aunt regards Heidi as an imposition, as she has to raise Heidi after her sister and brother-in-law die. Dete takes Heidi to live with Heidi's grandfather, Alm-Uncle, who is the father of Heidi's father. Her grandfather lives in Dorfli, where he maintains his distance from others and grazes livestock ("Alm" refers to the mountain ranges where he grazes his flock). Alm-Uncle grows to love Heidi, and she also gets to know Peter, a goatherd, and Peter's blind grandmother, Bridget (also called "Grannie"). 


Heidi later goes to Frankfurt to work as a companion to Clara Sesemann (spelled "Klara" in German), a sick girl who can't walk and who lives with her father, Mr. Sesemann. Heidi charms Clara with her friendliness and country manners. Fraulein Rottenmeier, Clara's housekeeper, is a strict woman who dislikes Heidi. Doctor Classen diagnoses Heidi with homesickness and sends her home to the mountains. 

Do you think coalition governments can be effective? What are some of the benefits and drawbacks of the coalition governing model?

Coalition governments, also known as consociational, or power-sharing governments, can be effective in the right circumstances. 


This type of government is popularly seen in Europe, in countries such as Switzerland and Ireland. The main benefit is that it gives members of the government from different ideologies the opportunity to work together in order to represent a larger portion of the population.


A strong example to back up the use of a coalition government is the case of India. India is comprised of 29 states, each representing a distinct culture, language, and history. In order to respect these differences, each state has some autonomy in its ability to create laws and establish an official state language and education system, among other factors. This has eased tensions between the states and the federal government, and the representatives of each state in India have the ability to speak for their states in the national government as well. This has all resulted in a stable Indian government where there is generally great pride in not only the home state of Indians but also in the idea of being "Indian" in a national sense as well.


Drawbacks to coalition government can often be seen when there are great ethnic or religious divides. One type of coalition government is that of "proportional representation." This is when, for example, there are two ethnic groups in a country--one has a larger population than the other: the group with a larger population will have a larger representation in the government (proportional to its population size). When there is already hostility between the two groups, this type of representation can spark outcry and often violence from the smaller and less represented group. In response to this initial upset, the other group will often react with violence as well, leading to war and/or a complete breakdown of the government. 


An example of a failure in a coalition government is the case of Lebanon. The power was divided between Christian, Sunni Muslim, and Shi'a Muslim populations in the 1940s. This arrangement unfortunately ended in civil war.


So in some cases, coalition governments can be effective, but there is always the risk, especially when forming a coalition between sensitive divisions, that the end result will be violence and war.

What are the differences between conceptual skills, human skills, and technical skills?

These are all valuable skills to have in any organization, and a good manager will have all three.  Let's go over them one at a time.


Conceptual skills are "thinking" kinds of skills. Our ability to look at the big picture is a conceptual skill. Our ability to see how all the parts make the whole is a conceptual skill, an understanding of relationships.  Our ability to generate and assess solutions to problems is sometimes a kind of conceptual skill.  Logic is a conceptual skill.  We need to understand cause and effect and analogy, which are two forms of logical analysis.  Critical thinking is a kind of conceptual skill in which one questions and assesses what one is presented with, rather than taking it as given.  Planning is a conceptual skill. 


Human skills are interpersonal and intrapersonal skills. That is, they are the skills we use to get along with other people and to understand ourselves, too.  Everyone needs needs both to get along in any social setting, but managers need them more than most because managers are responsible for motivating people to be as productive as possible and also for managing any conflict in the workplace.  The person who has no insight into others and him or herself will not do very well with this. Empathy is one very important kind of interpersonal skill. We can succeed better with people if we understand how they feel. Understanding oneself is equally important, to know one's weaknesses and strengths, so as to work on the weakness and capitalize on the strengths.  If I know that I am not at my best in the morning before my second cup of coffee, I would not want to hold an important meeting.  On the other hand, some people do their very best work very early.  If I am more introverted than extroverted, there are some more "social" tasks I might delegate to someone extroverted.  To be an effective manager, you must understand yourself and others.


Technical skills are sometimes thought of as mechanical skills, which embrace not only the nuts and bolts of traditional mechanics, but also today's technological skills.  Having these does not necessarily mean that a manager can fix the copier or get rid of the technology help desk. It does mean the manager needs to have a clue. A manager, for example, might be responsible for choosing new software for a company, in which case, the manager needs to have some idea how such software works and what it does.  A breakdown on the production line might not find the manager tightening the screw that worked itself loose, although there are many who would and do, but the manager has to have at least enough mechanical sense to know if the workers should be sent home or if the line can be operational in an hour.  It is difficult to manage any kind of mechanical or technological operation if one has no skills whatsoever in this area.


A good manager has many tools in the toolbox to draw upon, and these are the most important kinds of skills to have.  The manager who can excel in all three areas should be successful.

Monday, November 21, 2016

What does this mean: "Given a sizable tract in which to determine the optimum soil resistivity, some intuition is in order."

What this means is that you have an area of soil that is large enough to be mixed thoroughly, so that it can be considered uniform. In addition, the soil's resistivity means how much electrical resistance the soil loads in relation to a geometric constraint. 


Where it implies "intuition is in order," what it is looking for is some intelligence on your part. You must conjure a way in your mind to determine this resistivity. This may mean you need to devise an experiment to determine resistivity, or if the question is a real life application rather than theoretical, ask a proper authority for data on the soil.


If you must run an experiment, you can build a rig pretty easily at home for imprecise measurements by making a small box with electric contacts at both ends, measuring the base resistance across with a multimeter, and then filling the box with soil to take another measurement. More measurements can be made to build a data set. Finally, just measure the cross sectional area and box length to calculate the resistivity from the resistance and dimensions.

Saturday, November 19, 2016

What is a weakness with the legislative branch?

One weakness of the legislative branch is that it could be difficult to pass a law. We are seeing that scenario play out to some degree today. Because there are two houses of Congress, an issue may arise if a different political party controls each house of Congress. If those parties differ significantly over many issues, little might get accomplished. Additionally, if the President is from a different party than both houses of Congress, little might get done in this situation.


President Obama is from the Democratic Party while the Republicans control both houses of Congress. Because there isn’t a great working relationship between the President and the Congress, the threat of a presidential veto is always present. Since the Republicans don’t control two-thirds of both houses of Congress, it would be hard to override a veto. As a result, there has been some difficulty in reaching an agreement with proposed laws. At times, the President wanted to see a certain concept be put into a law. However, since Congress is controlled by the Republicans who didn't agree with the President about this concept, no action was taken and the idea never became a law. After the election in 2012, the Democrats controlled the Senate while the Republicans controlled the House of Representatives. Since these parties had very different opinions on various issues, there wasn’t a lot of agreement on bills, and many bills never got passed.


There are circumstances where the legislative branch is split between the parties that control each house, or the President is from a different party than the party that controls both houses of Congress. As a result, it becomes more difficult to a pass a law, which is one weakness of the legislative branch.

Describe a fad that has come and gone during your lifetime, such as Beanie Babies. Did you take part in the fad? Why or why not? How long did...

Back in the 1970's, there was a brief fad where people were buying "Pet Rocks." They came in a cardboard box that looked like the kind of thing you would carry a hamster home in from a pet store. They had an instruction booklet with tips for "training" the pet rock. 


While I was aware of the fad--I was a teenager--I did not take part in it. They sold for $4 and that was actually a decent amount of money. Also, I had very skeptical parents who would have pointed out that it was just a rock and I could pick up a rock anywhere for free. I knew better than to ask!


The Wikipedia article on Pet Rocks, cited below, says that the fad lasted about six months. They were really hot and well-known very suddenly and they dropped out of consciousness for the most part equally suddenly. 


Truly, this fad was unsustainable. After all, people began to recognize, as my parents did, that they were buying essentially nothing. The hot Christmas gift in 1975 began to gather dust in 1976. 


In actuality, I have seen lots of fads come and go, including Beanie Babies, Cabbage Patch Dolls, Elmo, and other things I can't even remember. These fads tend to play on people's emotions, which leads to them fighting each other at McDonald's for a Happy Meal prize, in the case of Beanie Babies. Eventually, logic starts to kick in and the "investments" people make in their collections of whatever become mostly worthless. 

Wednesday, November 16, 2016

What does Catherine want to show by pressing the electric bell?

The general answer to the question is that Catherine wants to show that she is a high status, cultivated person. If the question refers to her specific use of the bell in Act III, the answer is that she wants to summon a servant, and show herself to be cool, powerful, and unperturbed by the controversy of the coat.


Here are the particulars.


First, Catherine wants to be counted among the most cultured, civilized people. So while her husband, Petkoff,  is away at war, she has had an electric servant bell installed in her home. It's a complete novelty to Petkoff; he hasn't even heard of these devices, and asks her what it's for. Her answer clarifies what it means to her: It's an important act of conforming to ways of cultural elites.



CATHERINE. You touch a button; something tinkles in the kitchen; and then Nicola comes up.


PETKOFF. Why not shout for him?


CATHERINE. Civilized people never shout for their servants. I've learnt that while you were away.



Second, regarding Catherine's use of the bell in Act III, Catherine presses the button to summon Nicola so she can tell him to retrieve the coat from the blue closet. Using the bell allows Catherine to create a more dramatic effect -- highlighting her apparent calm and confidence. She might have called out for Nicola instead, or left the library to get the coat herself. But it seems clear that she is interested in making an impression as the cool, regal mistress of the house. After she presses the bell, and her husband questions her about it, the stage directions describe her confident, grand air:



She looks at him majestically and silently resumes her chair and her needlework.


What are the advantages and disadvantages of a long chain of command?

A long chain of command certainly does have advantages and disadvantages. Let's go over the most extreme example, the military.  A military organization has a general at the top and at the bottom is a private. It is the best example there is, I think, of a long chain of command. 


A few advantages come quickly to mind.  One advantage to this is that the span of control is not too wide. The general does not have to give direct orders to tens of thousands of privates at the bottom, just to the lieutenant general beneath him or her and so on down the line until a lieutenant or captain gets the orders, transmits them to a sergeant, who then tells the troops what to do.  Each person is responsible for a smaller number of people, which makes for much better management and control.  Another advantage is that the person at the top in such an organization is able to have a clear mind to think about the big picture, and strategize about what troops to deploy where, or how to eliminate the culture of sexual harassment.  At each level in a long chain of command, the responsibilities are delineated in a way that affords the person responsible the time and energy to focus on just those delineated responsibilities.  The Major does not worry about whether the cook is doing a good job or how many medics are attached to a particular unit. Someone below him or her has this concern.  Another advantage is in the way communication works. Privates who have complaints or suggestions do not call the general with them. They go through the chain of command.  This reduces the "clutter" at the top and is meant to ensure that the person at the top does not use all of his or her time putting out small fires, not the best use of time for a general. In the military, at least, this very long chain of command seems to instill discipline in the ranks quite effectively, perhaps because of the span of control and the communications mechanisms.


Disadvantages there certainly are, though. There is almost a complete lack of autonomy at the lower levels, so that decision-making is seldom localized.  This means that the people on the spot, closest to the facts, are usually unable to act.  They must await disposition from a higher level, which means that the best decisions are not always being made. Another disadvantage is in the long line of communication. There probably are some times that it would be good for a private to tell a general something, and this chain of command makes that a virtual impossibility.  Another disadvantage is that the people at the top can feel so removed from the people below that the people below are not as motivated as they could be.  Most people like to know whom they are working for, I think, and to see that person at least occasionally.  This is why generals do go around talking to troops, but it is unlikely that they ever get around often enough to really motivate people. 


These advantages and disadvantages exist just as much in civilian organizations as they do in the military, and if you think about a very large company, you will be able to see their application easily. 

Tuesday, November 15, 2016

Why does Eckels want to travel back in time?

Eckels wants to travel back in time to hunt and kill a dinosaur.  


Eckels is paying ten thousand dollars to be a part of a safari group going back in time.  The company that does this is Time Safari, Inc., and the expedition is being led by Mr. Travis.  


Eckels is not a character that readers are meant to like.  From the moment that we are introduced to him, it is clear that he is pompous and arrogant.  He waves around his check like it's a talisman of power and privilege.  



The muscles around  his mouth formed a smile as he put his hand slowly out upon the air, and in that hand waved a check for ten thousand dollars to the man behind the desk.



Eckels doesn't seem to realize that he will not be the only paying customer on the safari, because he uses "I" a lot instead of "we."  At one point, rules are being explained to Eckels about what he does and does not have to worry about.  He rudely interrupts the other man and says the only thing he (Eckels) has to worry about "is shooting my dinosaur."  Notice how Eckels believes that his check guarantees himself shooting rights.  


Of course as the reader comes to learn, Eckels is all talk.  Despite his brave bravado, he is the only safari member that runs in fear back to the time machine.  The T. rex is simply too scary for him.  



"Get me out of here," said Eckels. "It was never like this before. I was always sure I'd come through alive. I had good guides, good safaris, and safety. This time, I figured wrong. I've met my  match and admit it. This is too much for me to get hold of." 



He's so scared in fact, that he steps off of the path, kills a butterfly, and changes the future/present forever.  

Monday, November 14, 2016

In what ways does the narrative depict how Mrs. Sommers misses her life before she was married in "A Pair of Silk Stockings" by Kate Chopin?

In her story "A Pair of Silk Stockings," Chopin depicts how much Mrs. Sommers misses her former life by the delight she displays when she treats herself to personal luxuries.


Having lived under the constraints of motherhood, Mrs. Sommers is constantly worried about money and has had to sacrifice her desires for the necessity of providing for her children. Even then, she has had to compromise on many of the necessities for them, causing her life to seem banal. But, when she becomes the "unexpected possessor" of fifteen dollars, for the first time in a long time, Mrs. Sommers experiences a sense of freedom from having to budget this money. Nevertheless, she feels that she must spend this money for practicalities, such as hats for the children, shoes, and material for new shirts for the boys, and a new gown for her daughter.


On the day that she goes shopping, Mrs. Sommers has forgotten to eat; so, because she feels rather faint, she takes a seat at a lunch counter in a department store. There her hand brushes against "something very soothing, very pleasant to touch." It is a pile of silk stockings, and she cannot resist running her hand along them, feeling the soft, smooth material that glides through her fingers. When the clerk asks if she may help Mrs. Sommers, her resistance is gone; she asks for her size. 


After she purchases the stockings, Mrs. Sommers's hunger for small luxuries waxes and she goes to change out of her cotton stockings in the ladies' waiting room. "How good was the touch of the raw silk to her flesh!"


Admiring how pretty her ankles appear now, she goes to the shoe department and purchases new boots. And, after doing this, she moves to yet another counter where she fits her hands with kid gloves.


Having completely surrendered to her own pleasure, Mrs. Sommers spends the afternoon luxuriating in her new possessions, as well as attending a matinée. When the play is over and Mrs. Sommers must catch the trolley for home, "it was like a dream ended." But, she will treasure the memory of the day that she was again carefree.

What views on marriage does Charlotte Bronte present in her novel Jane Eyre?

Bronte (and Jane Eyre) believed that marriage should be a match between intellectual and spiritual equals. One of the things that made marriage difficult for Jane was the power (legal and sexual) it gave the husband over the wife. You can see these issues at work in the section towards the end of the book where Jane has to decide if she will marry St John: on the one hand, St John appeals to her sense of duty and self sacrifice, but ultimately she rejects him because of his evident pride, arrogance, and sense of superiority. Rochester, in contrast, has actually been trapped in a bad marriage; Bertha's power over him -- her existence! -- ruins his hope for "true love" with Jane. Rochester clearly does not consider Bertha to be his wife in any real way, but is unable to escape the legal and moral bonds of marriage. In a sense, Rochester has lived the experience Jane avoids with St John -- servitude to an unloving spouse. Jane ultimately marries Rochester because she believes that they are spiritual and intellectual equals -- Rochester, in his crippled state at the end of of the book, requires Jane's care, but Jane, for her part, requires Rochester's understanding. 

Sunday, November 13, 2016

What is the setting of the Watson's home in The Watsons Go to Birmingham--1963 by Christopher Paul Curtis?

The Watsons live in Flint, Michigan. As the story opens, as Kenny says, "it was about a zillion degrees below zero" (page 1). The family turns up their thermostat, but the furnace is making noises and seems like it's going to "blow up." To keep warm, the family is huddled together on the couch under a blanket. They are wearing scarves and other winter clothing. Outside is their car, a 1948 Plymouth (which is 15 years old), which they have named the Brown Bomber. The family is clearly close, and the father helps the family keep their minds off the cold by making jokes. Later, the family travels to Birmingham, Alabama, to bring their oldest son, Byron, to the house of Momma's mother, Grandma Sands, in an attempt to teach Byron how to show respect and manners. 

What do you think is the most interesting thing about 19th century European history? Why?

There would be several topics that you could consider in determining what might be the most important or most interesting event in Europe or affecting Europe in the 1800s. These topics could include the loss of colonies, the unification of countries, the planting of the seeds for the start of World War I, and wars in general.


One topic I would consider would be how some European countries lost some of their colonies in the 1800s. Both Spain and Portugal lost much of their empire in Central and South America. You certainly could highlight the revolutions that occurred in Brazil and Mexico to use as prime examples of lands Spain and Portugal lost. You could also add how the United States issued the Monroe Doctrine to keep the Europeans from returning to Central and South America. I would also mention how Great Britain used its navy to enforce the Monroe Doctrine since the enforcement of the Monroe Doctrine would weaken their rivals.


Another topic to consider would be the steps taken in the 1860s to allow Germany and Italy to unite their states into a unified country. You could focus on the actions of Otto von Bismarck in Germany and Cavour in Italy to help with or facilitate the unification process. I would also tie this topic in with how the unification of Italy and Germany helped plant the seeds for the start of World War I. Both countries wanted colonies, and there were few lands left to colonize. Thus, each country began to build up their military as they planned to attack the countries that had colonies. You could also mention how Germany got control of Alsace-Lorraine as a result of the Franco-Prussian War. France vowed to get this land back in the future.


There are many examples of wars that were fought in Europe in the 1800s from which you could draw your answer. In addition to the Franco-Prussian War, you could write about Napoleon’s plan to conquer Europe in the early 1800s. You could write about his many military successes and then focus on his crushing defeat in Russia and his final defeat at Waterloo. You could write about the Austro-Prussian War that gave Prussia control over the process of the unification of Germany.


There are many topics about which you could write to answer this question. Each of these events played a major role in European history in the 1800s. These events not only affected Europe, but also they affected the world.

In Animal Farm, what do the pigs sleeping in the beds represent?

In Chapter 6, the pigs move into Mr. Jones's home, and rumors begin to circulate that the pigs have been sleeping in Mr. Jones's bed. Disturbed, Clover thinks she remembers one of the Seven Commandments forbids animals from sleeping in beds. When Muriel reads the Fourth Commandment, it says, "No animal shall sleep in a bed with sheets" (Orwell 27). Squealer goes on to explain that it is perfectly okay for animals to sleep in beds, but the rule actually forbids animals from using sheets, which are a human invention. Squealer then explains it is essential for pigs to sleep in comfortable beds because they need rest to do all the "brainwork" needed to run Animal Farm. After hearing Squealer's explanation, the animals passively accept the Fourth Commandment and feel reassured.


The pigs sleeping in Mr. Jones's beds represents the pigs' lazy personalities, ongoing corruption, and creation of a widening inequality gap on the farm. Unlike the other animals on the farm who have to sleep outside or on bales of hay, the pigs sleep lavishly and comfortably inside the farmhouse. Orwell is depicting how the lower class is forced to suffer while the upper class lives in luxury. With the addition of "with sheets" written into the Fourth Commandment, Orwell portrays how language can be manipulated to benefit the ruling class. Beds are also associated with rest, and Orwell is suggesting the pigs are lazy. The pigs sleeping in Mr. Jones's bed represents their lethargic personalities that contrast with the work ethic of the other farm animals.

Saturday, November 12, 2016

How can a global project be more complex than a project performed within just one country? How might these elements affect the successful outcome...

In addition to having far more moving parts, a global project is far more complex than one within one nation because one must take into account the differences from one country to another. Let us consider a few of these.


First, if one is operating in more than one country, one must take into account cultural differences. These include language, dress, religion, and customs. Without having someone on the ground who speaks the language, it is difficult to operate. Even when someone does speak the language, there are bound to be local idioms that must be learned. In many Muslim countries, sending a woman with an uncovered head and bare arms to head a setup operation is, to put it mildly, a blunder. Scheduling an important meeting on a Saturday in Israel, the Jewish day of worship, is not going to win friends and influence people. In many countries with a hot climate, there is no work during the worst heat of the day. Trying to get a workforce to disregard this custom is a recipe for disaster. A global operation must account for a myriad of countries and cultures. 


Second, there is a political and legal environment that must be considered. To be successful, you cannot run afoul of the laws of the countries in which you want to operate. Sometimes, a political hierarchy must be considered, so that one approaches the powers that be in a given country in the proper order. In some countries, bribery is the norm, which makes it difficult for American companies to compete, as they are not permitted under American law to bribe in foreign lands. Whatever the laws are of the country in question, they must be obeyed, which makes global projects quite complex.  


Third, there are geographical considerations that make any project more complex. When a CEO is sitting in the office looking at a map, deciding to open five more factories in five different countries, he or she must consider the terrain, weather, flora and fauna, and, one hopes, the environmental impact. Is the company building on bedrock or sand? Could monsoons sweep a building away? Ebola or dengue fever might be rampant in the area. That surely should be something to consider. The site might need to be cleared of trees that should be preserved. Each country and each new site will create unique challenges for the project.


The global economy represents new and exciting opportunities for business, but it is vital to remember each country is different. The cultures, political and legal environments, and geographical features will always vary. Inevitably, this makes any project more complex than a project done solely in one's own country.

Friday, November 11, 2016

What are some similarities and differences of Abigail Williams, from The Crucible and Daisy Buchanan, from The Great Gatsby.

Daisy and Abigail are similar in that they are both greedy and selfish.  Daisy is unfaithful to her husband, having an affair with Gatsby; however, she then abandons Gatsby when she learns how he's made his fortune.  Further, she allows him to take the blame for the death of Myrtle Wilson, who she actually hit with Gatsby's car.  She takes as much as she can from him and then abandons him when he has nothing more to offer her.  Abigail is also greedy: she longs to have John Proctor, her former lover, to herself, and she doesn't care who else is hurt.  She begins the hysteria in the town of Salem, hysteria that leads to the deaths of dozens of innocents, all so that she can remove Proctor's wife and anyone else she doesn't like.  Then, realizing that she cannot have him, she abandons Salem to sink further into corruption.  Both women allow innocent people to die in pursuit of their own selfish desires.


Daisy and Abigail differ, however, in intention.  While Daisy is certainly greedy and selfish, she doesn't seem to really possess an awareness of her flaws; she has a certain innocence, a belief that she can return to the way things were with Gatsby.  Though she believes she is cynical in the beginning, she isn't really.  Once she is reunited with Gatsby, she does seem to really love him.  It's just that when she finds out that he's made his fortune illegally, as a bootlegger, he seems to become sort of subhuman to her: she seems to care as little about his life as she does about Myrtle Wilson's.  She intended to be with him out of love, but when she finds out how dramatically lower he is in status than she, it becomes clear that she prioritizes status over love, but she didn't set out to manipulate.  Abigail, on the other hand, seems to know exactly what she's doing, manipulating others consciously from the very first.  While Daisy seems to be blindly following whatever impulse she thinks will make her happiest, Abigail is very cunning and thoughtful: she is threatening and deceitful and murderous and all for one cause, one goal.  Daisy doesn't think ahead the way Abigail does; she isn't as manipulative. 

In the poem "Tears, Idle Tears" why does the poet Lord Alfred Tennyson describe tears as "idle"?

In the poem "Tears, Idle Tears" the designation "idle" is a bit obscure, because while the poet opens with the expression "Tears, idle tears, I know not what they mean," the main theme of the poem does not seem to be tears specifically, but rather regret and longing for the past.


The word "idle" typically refers to something that is inactive, indigent, stagnant, useless, or deliberately not fulfilling its designated occupation. In the poem "Tears, Idle Tears," the word "idle" seems to most closely fit the idea of "useless"—that is, something that exists but serves no purpose.


To understand the phrase "tears, idle tears" in this poem it is necessary to carefully consider the poem in its entirety.


Consider the ideas that are repeated in this poem. "Tears... rise in the heart... thinking of the days that are no more" (paragraph 1); "So sad, so fresh the days that are no more" (paragraph 2); "So sad, so strange, the days that are no more" (paragraph 3); "O Death in Life the days that are no more!" (paragraph 4).


Through these phrases it becomes apparent that the main theme in this poem is the poet's experience of deep sadness when considering the past—a grief that makes life itself feel like death (paragraph 4). The poet's tears, however, are "idle"—that is, they are useless, they are of no benefit. He grieves over the past, which by nature and definition cannot be changed or affected by tears or any other actions.

Wednesday, November 9, 2016

What is the significance of the title, Fahrenheit 451?

As we can see from Bradbury's addendum to the novel, the title refers to the temperature at which book-paper burns. The significance of this title becomes apparent once the novel begins: Montag, the main character, is employed as a fireman but, in the society of Fahrenheit 451, it is his job to start fires, not to put them out. Specifically, the firemen are responsible for burning books because their society is highly-censored and emphasises entertainment over learning.


In addition, this title is also significant because it is the first reference to fire, one of the novel's most potent symbols. In Fahrenheit 451, fire is a symbol of destruction and censorship: the firemen wear the number "451" on their uniforms, for example. But it also symbolises the death of one way of life and the beginning of a new one, as shown by Montag's transformation from committed fireman to social outsider.

Monday, November 7, 2016

What is the first thing that Scout finds in the oak tree on the edge of Boo Radley's property? How does Jem react when he learns about Scout's...

In Chapter 4, Scout is passing the Radleys' home and notices a shiny object coming from the knothole of the giant oak tree in the Radleys' yard. Scout runs over to the tree and grabs two sticks of Wrigley's Double-Mint chewing gum out of the knothole. When she gets home, she unwraps the gum and sniffs it to make sure it isn't poisonous. Jem returns home and asks Scout where she got the wad of chewing gum. Scout tells Jem she found it sticking out of the tree in the Radley yard and Jem yells at her to immediately spit out the gum. Scout obeys Jem by spitting out the gum and then informs him she's been chewing it all day. Jem is still under the impression that everything associated with the Radleys is harmful and tells Scout she's not even supposed to touch the Radleys' trees, let alone eat anything she finds in them. Jem insists what Scout did was deadly and commands her to gargle the taste out of her mouth.

Who is the middleman in marketing?

Marketing is an important business function. Marketing is responsible for product development, distribution, pricing, and promotion. Distribution ensures the product or service is delivered to the consumer. In distribution, middlemen are responsible for bringing the product closer to the customers.


Brokers purchase products from sellers at a low price. They later sell the product to the consumer at a higher price. The middlemen assume all the risks associated with the product as it moves along the distribution channel. The risks borne by the brokers are used to justify the higher prices to the consumers. In some situations, the middlemen do not handle the product; rather, they directly connect the buyer to the seller.


Wholesalers and retailers are examples of middlemen. They purchase the product in bulk and at a low price. They later sell the product at a higher price and in quantities required by the consumer.

Saturday, November 5, 2016

Would "rising in thunderheads of tobacco smoke" be an example of personification or a metaphor?

The quote in the question is an example of a metaphor.  A metaphor is a comparison of two unlike things and does not use the words "like" or "as."  In this case, the quote being used is describing the smoke that is surrounding Captain Beatty.  The smoke isn't thin wisps of tobacco smoke.  It's as thick as the biggest and most dangerous storm clouds.    



Captain Beatty there, rising in thunderheads of tobacco smoke.



The comparison being made portrays Captain Beatty and his movements as similar to a big, powerful storm cloud.  He is imposing and dangerous looking.  Because the quote says that Beatty is in the cloud, I picture Beatty as enshrouded by the cloud.  The line gives Captain Beatty a sort of Satanic presence, which is exactly the kind of person that he is.  He is the ruthless, malicious, shrewd, and destructive antagonist of the story.  At times he comes across as friendly and soft, but that is only to gain an advantage over some other person.  

What are the similarities between the poet Robert Frost and his poem "The Road Not Taken"?

At least three similarities are apparent between the poet Robert Frost and the speaker in "The Road Not Taken": (1) leaving Vermont to go to England in search of a publisher for his poetry (having left farming only because of his grief over the death of his daughter at his farm in Derry); (2) choosing between two things, farming and poetry, perceived at one time as equally common and at another as unequally so; (3) choosing poetry made all the difference for Frost, for poetry allowed him to tame his mind and emotions.

The poem starts with the line "Two roads diverged in a yellow wood,...." Frost came to two roads diverging when, needing to make a living for his family and to leave his grief over Elinor's infant death behind him, he chose to seriously pursue a career as a poet, taking his family from rural woodland Vermont to England.

Stanza three ends with, "the passing there / Had worn them really about the same," (he says this despite the "undergrowth" at the bend of the path he did not choose). From his troubled circumstance in 1912, staying as a farmer or leaving as a poet may have presented equal perspectives to him; although "undergrowth" suggests a preference for the "grassy" way he did choose, which was England and an English publisher and audience. As an aside, one reason he opted for England was that he met with criticism from American academia because he wrote in traditional meter and rhyme instead of abandoning it for modernist poetic style.

The famous ending of this poem--published in 1916 in the collection Mountain Interval before Frost had won his first Pulitzer in 1924--says, "I took the one less traveled by, / And that has made all the difference." For Frost, his choice of taking the road of poetry did make all the difference because, as biographer Jay Parini said, his poetry, with its highly developed structure, allowed him to keep his demons of depression and self-doubt in check. It is at this point, the point of hindsight, that he confesses that the road he chose was indeed "one less traveled by."



Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.


Friday, November 4, 2016

In Emma by Jane Austen, what does the first sentence say about how Austen portrays Emma Woodhouse, and which themes are revealed in the first...

In the first sentence of Emma, Austen says that her heroine is beautiful, smart, and wealthy and has a good personality and that she has lived her 21 years without much to disturb her. The first sentence relates to way in which Austen portrays Emma Woodhouse and to the themes of the novel. Emma's life as a young woman in Regency England has led her to be cloistered and naive. Though she is bright, she does not know much about life and must become more enlightened through experience and through connections with men in her life, such as Mr. Knightley, who have been allowed to have more experiences in the outer world. Emma's naiveté leads her to meddle in other people's affairs, such as Harriet's relationships with Mr. Elton and Mr. Martin, in flawed ways. Her lack of experience also causes her to judge other people, such as Jane Fairfax, unfairly. Though her friendship with Mr. Knightley and her experiences with others, Emma is eventually able to cultivate her considerable intelligence and charm into a more worldly approach to life. 

In Jane Austen's Mansfield Park, how does Henry's character develop or remain the same throughout the novel? What is the relationship between...

Henry Crawford's character remains the same throughout the novel, though there is a time when he seems on the road to reforming himself. Henry is a bored, wealthy, worldly young man who comes with his sister Mary to stay with their half-sister at the Mansfield parsonage. At first dismissed by Julia and Maria Bertram as not being good looking, he is soon able to use his considerable confidence and charisma to charm them, and he enters into an open flirtation with both in order to amuse himself. Their poor relation, cousin Fanny, is especially shocked at the open flirtation between Maria and Henry because Maria is engaged to another man, the wealthy but socially inept Rushworth.


When Maria marries and Julia goes with her on her honeymoon, Henry decides to amuse himself by making the timid Fanny fall in love with him, hoping, as he confides in Mary, to put a hole in her heart. Instead, Fanny's avoidance and obvious dislike of him, along with her beauty and virtue, cause him to fall in love with her. At this point, it seems the callous rake might reform: he proposes marriage to Fanny and, impressed by her virtue, seems to want to do good, at least to her. Fanny, however, at first thinks the proposal is a cruel joke and later refuses to marry him, knowing what he is. Her rejection only inflames his ardor and determination to win her. When she is banished to Portsmouth, he continues to court her.


But the seeming change of character is only the whim of the moment: Henry soon returns to his selfish ways, seducing the married Maria Bertram and running off with her, and embroiling the entire Bertram family in scandal. He is true to form: he can't stand being rejected and, in society, Maria is cold to him. His own ego at the moment is more important to him than his future contentment or what happens to Maria: he is willing to ruin her life.


Henry is best characterized as the consummate shape shifter, the man who can assume any role to perfection, the serpent in the garden. 


Mary and Henry, growing up together in a hard, dysfunctional household full of "rears and vices," a pun on the ranks of admirals, are extremely close, and Mary works as Henry's co-conspirator in seducing Fanny. Both are worldly, well-socialized and charming, and both have so internalized the materialist and hedonistic values of London society that they have lost their moral compasses. Both throw away happiness through lack of moral imagination.


The key thematic point about Henry's character is not that it changes, because it doesn't, although there is a point where he seems to dimly perceive that Fanny's virtue and her brother William's willingness to work hard to advance in the navy represent a way of life that might be more satisfying than his bored existence filled with idle amusements. The main point is that other people's perceptions of him change based on their own needs and situations. Fanny, for example, while banished to crowded quarters with her dysfunctional family in Portsmouth, begins to waver on Henry and think he may not be so bad a character: environment, Austen says, influences how we perceive others. 

What was the weak point of the young man's story in "Dusk"?

The young man who sits down on the bench beside Norman Gortsby tells him that he couldn't find his hotel after going out to buy a cake of soap. Since he had left most of his money in his hotel room, he now only had a couple of pennies in his pocket after paying for the soap and a drink at a pub. Then the young man makes his pitch.



"Unless I can find some decent chap to swallow my story and lend me some money I seem likely to spend the night on the Embankment."



Gortsby is accustomed to sitting on these park benches at dusk and, consequently has been approached by many strangers with hard-luck stories. He senses this will be another one of them and has no intention of parting with any money. But he lets the young man tells his whole story because it amuses him and because he is a little sadistic. Then:



"Of course," said Gortsby slowly, "the weak point of your story is that you can't produce the soap."
     The young man sat forward hurriedly, felt rapidly in the pockets of his overcoat, and then jumped to his feet.
     "I must have lost it," he muttered angrily.
     "To lose an hotel and a cake of soap on one afternoon suggests wilful carelessness," said Gortsby, but the young man scarcely waited to hear the end of the remark. He flitted away down the path, his head held high, with an air of somewhat jaded jauntiness.



The young con-man is miffed to realize that he has been wasting his valuable time. It is already dusk, and the park will soon be depopulated. The fact that he hadn't had the foresight to purchase a cake of soap suggests that he is a novice who has just recently thought of an idea which could make him a pound a day rather than the pound a week he would be earning as a typical office clerk. No doubt he would have subsequently bought a cake of soap to have to show his next prospect if he should be asked for proof. But Gortsby has found the cake of soap dropped by his bench by the elderly gentleman, and he has given it to the young apprentice con-artist along with a gold sovereign.


The story had been crafted in such a way that it would suggest that Gortsby was being given an opportunity to make a friend of a young country gentleman who didn't know a soul in London and who might be expected to show his gratitude by inviting him to lunch and perhaps inviting him down to his parents' manor house for a weekend of riding and shooting. The con-man was only asking for a short-term loan. He supposedly had plenty of money but couldn't get at it until tomorrow because he couldn't find his hotel. And meanwhile it was dusk and darkness was closing in. Gortsby, who was something of a connoisseur of hard-luck stories, reflected that the young stranger's pitch was really very good.



"It was a pity," mused Gortsby; "the going out to get one's own soap was the one convincing touch in the whole story, and yet it was just that little detail that brought him to grief. If he had had the brilliant forethought to provide himself with a cake of soap, wrapped and sealed with all the solicitude of the chemist's counter, he would have been a genius in his particular line. In his particular line genius certainly consists of an infinite capacity for taking precautions."


Thursday, November 3, 2016

Bartlet Financial Services Company holds a large portfolio of debt and stock securities as an investment. The total fair value of the portfolio at...

Basic accounting standards, regulated by the SOX (Sarbanes-Oxley Act), COSO and the SEC, govern how debt and security investments are reported by corporations. While there are advanced complex considerations--like relevance and reliability, comparability and consistency, and periocity and matching--that affect real-world accounting situations, basic accounting decisions are regulated by law, and violations can result in charges of financial manipulation and fraud as in the 2015 case of the SEC (Securities Exchange Commission) against the Computer Sciences Corporation, who were charged with a $190 million penalty. Further, while real-world debt and security investment accounting present subtleties and complexities, it is professional and personal ethics that provide the foundation for applying regulated basic accounting standards (Kermis & Kermis, "Financial reporting regulations, ethics and accounting").

Ethical Accounting: Intent
The underlying standard of accounting for debt and security investments is intent: "accounting for investments in the debt and equity securities ... requires management to categorize the securities based on the intent for holding the investment" (Judy Laux, "Investment in Securities"). Along with following basic accounting standards, in order for either Faust or McCabe to perform investment accounting ethically, they must categorize legitimately according to actual intent for holding any given debt or security investment.

Accounting Treatment for Trading versus for Available-for-Sale
Securities held with the intent of trading--meaning that they are held with the aim of selling when the value of the security increases, generating a short-term profit for the corporation--have their present market values reported on the balance sheet, through the step of year-end adjustments, in addition to having gains and losses (of original market value and present market value) reported on the income statement; this is regardless of whether the trading security has been sold or is still held. Thus this accounting entry on the income statement has ramifications for year-end profitability reporting. In contrast, securities held with the intent of available-for-sale are not reported on the income statement at all. Available-for-sale investments are reported only on the balance sheets in the stockholders' equity section (as an asset value for stockholders); compare this to trading investments being reported on the balance sheet as year-end adjustments. Accounting treatment differences for trading and available-for-sale investments do not affect corporate earnings.
 
Faust and McCabe: Ethical or Unethical
Faust, the Financial VP, and McCabe, the Financial Controller, want to classify the investments based on increased and decreased values and on their effects on present or future year income. On the face of it, this is an unethical approach that ignores intent for holding an investment, thus violating the accounting standard requiring classification of investments as trading or available-for-sale based upon intent for holding. Additionally, choosing to classify based on income projections for varying years may affect stockholders who may gain or lose asset value based upon the classification decisions.

Stakeholders
Stakeholders are a larger, more comprehensive group than stockholders, including sub-groups or individuals that can either affect or be affected by decisions made by the corporation; some stakeholders are the government, boards of directors, unions, community members and individual securities investors.

Year-End Net Income
On the face of it, classifying debt and security investments to optimize selectively chosen year-end incomes has the same ethical problems mentioned above: regulated basic accounting standards established by SOX and COSO (Committee on Sponsoring Organizations) and the SEC, require that classification of debt and security investments be made based on intent for holding the investment. Making classifications on other, arbitrarily chosen income advantages violates this fundamental basic accounting standard requirement.

find square roots of -1+2i

We have to find the square root of `-1+2i` i.e. `\sqrt{-1+2i}` We will find the square roots of the complex number of the form x+yi , where ...