Complex Number System Arithmetic
A complex number is an expression in the form: a + bi where a and b are real numbers. The symbol i is defined as √ 1. a is the real part of the complex number, and b is the complex part of the complex number. If a complex number has real part as a = 0, then it is called a pure imaginary number. All real numbers can be expressed as complex numbers with complex part b = 0. -5 + 2i 3i 10 real part –5; imaginary part 2 real part 0; imaginary part 3 real part 10; imaginary part 0 complex number pure imaginary number real number

Addition and Subtraction To add/subtract two complex numbers, add/subtract the real part of the first number with the real part of the second number. Then add/subtract the imaginary part of first number with the imaginary part of the second number. 4 2 6 4 5 4 —2 3 4 6 2 4 5 2 4 3 2 – 6i 7 – 7i Multiplication To multiply two complex numbers, set up the complex numbers like two binomials and use the distributive property for binomials (FOIL method). Then use the fact that 1, and collect like terms. 3 2 · 4 12 3 8 2 12 3 8 2 1

− 14 + 5i

Complex Conjugate If is a + bi complex number, then it’s complex conjugate is a – bi. To form the conjugate of a complex number, simply negate the sign of the imaginary part of the complex number. One of the properties of the conjugate is that if you multiply a complex number by it’s conjugate, the result is a real number. Complex Complex Number Conjugate 2 – 4i 2 + 4i –3 + 2i –3 – 2i Division To divide two complex numbers, arrange the complex numbers into a fraction with the divisor as the numerator and the dividend as the denominator. Next, multiply the top and bottom of the fraction by the complex conjugate of the denominator, and collect like terms. 5 3 1

...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...

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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...

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Abstract
A complexnumber is a number that can be written in the form of a+bi where a and b are real numbers and i is the value of the square root of negative one. In the form a + bi, a is considered the real part and the bi is considered the imaginary part. The goal of this project is show how the use of complexnumbers originates in the history of mathematics.
Introduction
Complex...

...ComplexNumbers
All complexnumbers consist of a real and imaginary part.
The imaginary part is a multiple of i (where i =[pic] ).
We often use the letter ‘z’ to represent a complexnumber eg. z = 3 +5i
The conjugate of z is written as z* or [pic]
If z1 = a + bi then the conjugate of z (z* ) = a – bi
Similarly if z2 = x – yi then the conjugate z2* = x + yi
z z* will always be real...

...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,...