1.1 Introduction : A **complex number**, in mathematics, is a number consisting of a real number part and an imaginary number part. It is written in the form a + bi, where a and b are real numbers, and i is the square root of minus one. Complex numbers are useful abstract quantities that can be used in calculations

1.1.1 Imaginary Numbers: Numbers whose square roots are negative are known as Imaginary numbers.

**Example: **√-1 , √-2

Imaginary number √-1 is denoted by the greek letter ‘i’ called iota.

**1.1.2 Powers of i**: i^{0} = 1; i^{2} = -1 ; i^{3} = -i ; and i^{4} = 1

For any two real numbers a & b;

√a × √b = √ab is true only when at least one of a and b is either 0 or positive.

Also,

√-a ×√-b = (i√a)(i√b) = i^{2} √ab = - √ab

Where a and b are positive real numbers.

In a complex number

Z = a + ib

a and b are the real numbers i is the imaginary number. a is the real part and b is the imaginary part and are written as ;

Re(z) = a

And

Im(z) = b

The set of complex numbers is given by:-

C = {z:z= a + ib, where a, b є R}

Example: In (4 +6i)

Re(z) = 4

And,

Im(z) = 6

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