# Introduction to imaginary numbers

### Introduction to imaginary numbers

Have you ever run into a situation where you want to find the square root of a negative number, but the calculator gives you nothing but a big error? Well, we will explore the meaning of this error from a different perspective. In this section, we will introduce the notion of imaginary numbers, and how to simplify them.

#### Lessons

• 1.
Simplify the roots of negative numbers

$\blacksquare\;$ $\sqrt{-16}$
$\blacksquare\;$ $\sqrt{-40}$
$\blacksquare\;$ $(-9)^{\frac{3}{2}}$

• 2.
Simplify the following imaginary numbers with high powers

$\blacksquare\;$ $i^5$
$\blacksquare\;$ $i^{200}$
$\blacksquare\;$ $(\frac{3i}{2})^4$