Wednesday, 22 February 2012

Properties of Complex Numbers

Previously we have discussed about system of equations worksheet and Today we are going to discuss about the Complex numbers and their properties which comes under andhra pradesh education board. First of all we should know about the complex numbers. A complex number is a number which has a form of x + iy, here x and y are the real numbers and i is known as the imaginary part or unit of the complex number. The value of i is root of -1 or i>2= -1. In the form of the complex number the term x is the real part and iy is the imaginary part of the number. The complex number is known as purely imaginary number if its real part or x is equals to 0.(Know more about Complex Numbers in broad manner, here,)
Now here I will tell you about some of the Properties of Complex Numbers:
1.    Powers of   i = root of -1, i>2 = -1, i>3 = -1, i>4 = 1
2.     Equality of two complex numbers: Two complex numbers are said to be equal if their real and imaginary parts are equal say two complex numbers are
 x + iy = a + ib if x = a and y = b.
3.    Addition property: When we add two complex numbers then we have to add the real parts to one another and imaginary parts to one another of the numbers. Like if we have two complex numbers say a + ib and x + iy then their addition will be (a + x) + (b + y)i.
The subtraction is just opposite of the addition property of the complex numbers.
4.    Multiplication: To multiply two complex numbers simply use the FOIL method.
(a + bi)*(x + yi)= (ax - by) + (ay + bx)i.
5.     Complex Conjugation: The complex number x + yi can be conjugate and it will give value x –yi. One thing is to remember is that the product of a complex number and its conjugate is always a real value. That is (x + iy) (x - iy)= x2+ y2.
So these are the Complex Number Properties. In the next topic we are going to discuss Properties of Numbers and if anyone want to know about Solving Binomial Expansion then they can refer to Internet and text books for understanding it more precisely and if you need help with math you can visit our website.

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