Division by a complex number is a very similar process to ‘rationalising’ surds – we call it ‘realising’

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Argand Diagrams

We can represent complex numbers on an Argand diagram. This similar to a normal set of x and y axes except that the x axis represents the real part of the number and the y axis represents the imaginary part of the number.

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The argand diagrams allow complex numbers to be expressed in terms of an angle (the argument) and the length of the line joining the point z to the origin (the modulus of z). Hence the complex number can be expressed in a polar form. The argument is measured from the real axis and ranges...

...Introduction
The purpose of this research paper is to introduce the topic of “Complex and ImaginaryNumbers” and its applications. I chose the topic “Complex and ImaginaryNumbers” because I am interested in mathematics that is hard to be pictured in your mind, unlike geometry or equations.
An imaginarynumber is the square root of a negative number. That is why they are calledimaginary, what René Descartes called them, because he thought such a number could not exist. In this paper, I will discuss how complex numbers and imaginarynumbers were discovered, the interesting math of complex numbers, and how they are used in other areas of mathematics and science. Complex numbers are applied in engineering, control theory and improper integrals to take the place of certain imaginary values, as well as to simplify some explanations.
2. THe Concept
2.1 History of imaginarynumbers
Long ago in ancient Greece, there was a society of mathematicians called Pythagoreans who believed the only numbers were natural numbers and positive rational numbers (Rusczyk 357). Later, Hippasus discovered irrational numbers such as√2, then 0 and negative numbers were...

...a time, in the imaginary land of numbers… Yes, numbers! I bet that would’ve never come to mind. Which brings me to the question: Who thought of them and why?
In 50 A.D., Heron of Alexandria studied the volume of an impossible part of a pyramid. He had to find √(81-114) which, back then, was insolvable. Heron soon gave up. For a very long time, negative radicals were simply deemed “impossible”. In the 1500’s, some speculation began to arise again over the square root of negative numbers. Formulas for solving 3rd and 4th degree polynomial equations were discovered and people realized that some work with square roots of negative numbers would occasionally be required. Naturally, they didn’t want to work with that, so they usually didn’t. Finally, in 1545, the first major work with imaginarynumbers occurred.
In 1545, Girolamo Carding wrote a book titled Ars Magna. He solved the equation
x(10-x)=40, finding the answer to be 5 plus or minus √-15. Although he found that this was the answer, he greatly disliked imaginarynumbers. He said that work with them would be, “as subtle as it would be useless”, and referred to working with them as “mental torture.” For a while, most people agreed with him. Later, in 1637, Rene Descartes came up with the standard form for complex numbers, which is a+bi. However, he didn’t like complex...

...History of imaginarynumbers
I is an imaginarynumber, it is also the only imaginarynumber. But it wasn’t just created it took a long time to convince mathematicians to accept the new number. Over time I was created. This also includes complex numbers, which are numbers that have both real and imaginarynumbers and people now use I in everyday math.
I was created because everyone needed it. At first the square root of a negative number was thought to be impossible. However, mathematicians soon came up with the idea that a number to solve this equations could be created. Today the square root of negative one is known as I. I is very useful to the world engineers use it to study stresses on beams. Complex numbers help us study the flow of fluid around objects, such as water around a pipe. Last year in my electricity class we had to use imaginarynumbers all the time.They are also used in electric circuits, and help in transmitting radio waves. So if it weren’t for I, we might not be able to talk on our cell phones, or listen to the radio. It is definitely a good thing that I was created.
The very first mention of people trying to use imaginarynumbers dates all the way back to the 1st century. Heron of...

...The numbers are overwhelming: Over the next 17 years, 350 million rural residents (more than the entire U.S. population today) will leave the farm and move to China’s cities. That will bring the Chinese urban population from just under 600 million today to close to 1 billion, changing China into a country where more than two-thirds of its people are city dwellers, says Jonathan Woetzel, a director in McKinsey’s Shanghai office. The change will reverse China’s centuries-old identity as a largely rural country. Thirty years ago, when China started modernizing its economy, more than 80% of Chinese lived in the countryside. And just six years ago it still was about 60%. Today China is just under 50% urban.
The newly urbanized population will live in eight megacities, those with a population of more than 10 million, as well 15 big cities with populations between 5 million and 10 million. In addition, by 2025 China will probably have at least 221 cities with a population over 1 million, estimates Woetzel. That compares with 35 cities of that scale across all of Europe today. These new urbanites are expected to be a powerful booster of growth: Urban consumption as a share of gross domestic product will most likely rise from 25% today to roughly 33% by 2025. “Urbanization is the engine of the Chinese economy—it is what has driven productivity growth over the last 20 years,” says Woetzel. “And China has the potential to keep doing this for the next 20 years.”...

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Assignments Requirements
1. Look up the definition of functional dependency. Can you find a good example?
In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database.
Cars
Suppose one is designing a system to track vehicles and the capacity of their engines. Each vehicle has a unique vehicle identification number (VIN). One would write VIN → Engine Capacity because it would be inappropriate for a vehicle's engine to have more than one capacity. (Assuming , in this case, that vehicles only have one engine.) Transversely, Engine Capacity → VIN is incorrect because there could be many vehicles with the same engine capacity.
This functional dependency may suggest that the attribute Engine Capacity be placed in a relation with candidate key VIN. However, that may not always be appropriate. For example, if that functional dependency occurs as a result of the transitive functional dependencies VIN → Vehicl e Model and Vehicle Model → Engine Capacity then that would not result in a normalized relation.
http://en.wikipedia.org/wiki/Transitive_dependency
2.Look up the definition of transitive dependency. Can you find a good example?
In Database Management System, a transitive dependency is a functional dependency which holds by virtue of transitivity. A transitive dependency can occur only in a relation that has three or more attributes. Let A, B, and C designate three distinct...

...Writing about Literature
Reading literature like Beowulf and Emerson’s "Heroism" is just one stop along the way to becoming an English scholar. Writing about literature is a third essential element. In the assignment for this lesson, you will synthesize the texts you have read to write a short essay; this means you will combine details from Beowulf and "Heroism" to show your understanding.
When writing about what you’ve read, you need to consider the general idea of the text and the specific pieces of it that will support your ideas. Asking yourself two questions can help you locate supporting evidence in the text.
Ask yourself
Which words, phrases, and sentences did the author select to make me think or feel this way about the text?
Why are those words, phrases, and sentences effective in making me think or feel the way I do about the text?
The first question will help you identify examples, details, or facts to support your central idea. The second question will help you provide the explanation of how your examples and details prove your point.
Supporting Your Ideas
When using supporting information from a text, you need to include:
· examples
· details
· facts
· explanations
You can incorporate these items in your writing in three ways:
Summarizing
Putting the main, broad ideas of a text entirely in your own words
Paraphrasing
Putting a specific sentence or several sentences entirely in your own words
Directly Quoting
Using the...

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When everything around you seems so routine and mundane, switch it up a little and think outside the box. Being known as simple, boring and everything that is done is expected, there is no room for excitement. Well all of that changes, except for the eyes of those on the outside looking in. Living double lives, both are extreme opposite of each other and both are extremely satisfying in their own right. Unfortunately they don’t play hand in hand, and the secrecy of one determines the success of the other and vice versa.
Inspiration
My inspiration came from the show “The Covert Affair”. The title moerso than the show grabbed my attention and was ultimately where I pulled inspiration from. It stems off of the basis of living double lives and pulling it off without anyone knowing but you. I have put a twist on it, allowing my target market to have a very diverse wardrobe, going from one extreme to the next. I have included tailored pants suits as well as dresses in my collection, depicting a very strong and structured woman. She is set in her career, yet lives a fun life, surrounded by friends and family. But they are also much like herself, safe and secure in their comfort zone. When night time falls, she becomes someone else. She is having a secret affair with excitement, with danger, with city nightlife, with fun and with herself!! Her wardrobe is no longer safe, her friends are not the same, her family has no clue that she is prowling the...

...inflation such as current purchasing power accounting, current cost accounting and continuously contemporary accounting which was not supported by the accounting professions, IASB has undertaken the work to develop conceptual frameworks for accounting.
The FASB in the US which developed one of the first conceptual frameworks in accounting defined its conceptual framework as ‘a coherent system of interrelated objectives and fundamentals that is expected to lead to consistent standards’. (Statement of Financial Accounting Concepts No 1: Objectives of Financial Reporting by Business Enterprises, 1978)
According to FASB, the conceptual framework ‘prescribes the nature, function and limits of financial accounting and reporting.’
According to the Exposure Draft (p12) publishes in 2008, the conceptual framework is:
‘a coherent system of concepts that flow from an objective. The objective of financial reporting is the foundation of the framework. The other concepts provide guidance on identifying the boundaries of financial reporting; selecting the transaction, other events and circumstances to be represented; how they should be recognised and measured (or disclosed); and how they should be summarised and communicated in financial reports.’
When developing the conceptual frameworks, there is a need to develop some consensus on important issues such as what is meant by financial reporting and what should be its scope; what...