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...

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Complex Laws.
Let z1 = a + ib, and z2 = c + id, where a, b, c and d are real numbers.
Square root of a complexnumber.
Solve for x and y by inspection. If unable to do through inspection use the identity;
And then perform simultaneous equations.
Conjugate.
If then .
Adding vectors.
Complete Parallelogram Head to Tail
Subtracting vectors.
Complete...

...Counting Number :
Is number we can use for counting things: 1, 2, 3, 4, 5, ... (and so on).
Does not include zero; does not include negative numbers; does not include fraction (such as 6/7 or 9/7); does not include decimals (such as 0.87 or 1.9)
Whole numbers :
The numbers {0, 1, 2, 3, ...}
There is no fractional or decimal part; and no negatives: 5, 49 and 980.
Integers :
Include the negative numbers...

...introduce the topic of “Complex and Imaginary Numbers” and its applications. I chose the topic “Complex and Imaginary Numbers” because I am interested in mathematics that is hard to be pictured in your mind, unlike geometry or equations.
An imaginary number is the square root of a negative number. That is why they are called imaginary, what René Descartes called them, because he thought such a...

...Prandtl Numbers
in the Stokes Problem for a Vertical Porous Plate
Basant K. JHA and Clement A. APERE
J. Phys. Soc. Jpn. 81 (2012) 064401
# 2012 The Physical Society of Japan
Person-to-person distribution by the author only. Not permitted for publication for institutional repositories or on personal Web sites.
FULL P APERS
Journal of the Physical Society of Japan 81 (2012) 064401
DOI: 10.1143/JPSJ.81.064401
MHD Natural Convection Flow of Fluids of Diﬀerent...

...The story "My Oedipus Complex" by Frank O'Connor deals exclusively with a little boy named Larry and his feelings towards his father. When his father returns home from World War II, Larry is resentful and jealous of losing his mother's undivided attention, and finds himself in a constant struggle to win back her affections.
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<br>I really enjoyed "My Oedipus Complex," because it reminded me a great deal of my elementary school days. My brother Brian was born...

...would be without irrational numbers? If the great Pythagorean hyppasus or any other mathematician would have not ever thought of such numbers?
Before ,understanding the development of irrational numbers ,we should understand what these numbers originally are and who discovered them? In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b,...

...and even business opportunities. Jealousy is an extremely prominent element in most of Frank O'Connor's writings and is often shown through different literary concepts such as conflict, characterization, and obsessive love. In writing “My Oedipus Complex”, O'Connor investigates the issue of jealousy through the various actions of his characters and the conflicts they get themselves tangled in, more importantly the ones involving their childlike obsessive love.
To fully...