﻿ Complex Numbers, Defined, with examples and practice problems Unfortunately, in the last year, adblock has now begun disabling almost all images from loading on our site, which has lead to mathwarehouse becoming unusable for adlbock users. # Complex Numbers

Overview: This article covers the definition of complex numbers of the form $$a+ bi$$ and how to graph complex numbers.

#### What are complex numbers?

A complex number can be written in the form a + bi where a and b are real numbers (including 0) and i is an imaginary number.

Therefore a complex number contains two 'parts':

• one that is real
• and another part that is imaginary

note: Even though complex have an imaginary part, there are actually many real life applications of these "imaginary" numbers including oscillating springs and electronics.

### Examples of a complex number

$$\begin{array}{c|c} \blue 3 + \red 5 i & \\\hline \blue{12} + \red{\sqrt{-3}} & \red{\sqrt{-3}} \text{ is the } \blue{imaginary} \text{ part} \\\hline \blue 9 - \red i & \\\hline \blue{12} - \red{\sqrt{-25}} & \red{\sqrt{-25}} \text{ is the } \blue{imaginary} \text{ part} \\\hline \end{array}$$

#### How do you graph complex numbers?

Complex numbers are often represented on a complex number plane (which looks very similar to a Cartesian plane). ### Practice Problems of complex number

##### Problem 1 ##### Problem 2

This complex number is in the fourth quadrant. ##### Problem 3

This complex number is in the 2nd quadrant. ##### Problem 4

This complex number is in the 3rd quadrant. 