# Introduction To Complex Numbers

**Introduction to complex numbers**

#### Numbers can be divided into two types:

- Real numbers
- Complex numbers

Here we are going to study complex numbers (imaginary number)

A number which can be represented in the form **a+ib **where a,b are real numbers

For the complex number

**Z= a+ib **where

**a** is called real part and is denoted by **Re z**

**b **is called imaginary part and is denoted by** Im z**

Of the complex number **z.**

**For example,**

**Z= 3+4i**

**3 **is called real part and **4 **is called imaginary part.

**Properties of complex numbers**

- Addition of two complex numbers is a complex number.
- Difference of two complex number is a complex number
- Product of two complex numbers is a complex number.

**For example,**

Let z=a+ib and z'=c+id then zz' is

ZZ'= (ac-bd)+i(ad+bc)