# The imaginary unit i

4 videos
1 skill
This is where math starts to get really cool. It may see strange to define a number whose square is negative one. Why do we do this? Because it fits a nice niche in the math ecosystem and can be used to solve problems in engineering and science (not to mention some of the coolest fractals are based on imaginary and complex numbers). The more you think about it, you might realize that all numbers, not just i, are very abstract.

### Introduction to i and imaginary numbers

VIDEO 5:20 minutes
Introduction to i and imaginary numbers

### Calculating i raised to arbitrary exponents

VIDEO 6:20 minutes
Calculating i raised to arbitrarily high exponents

### Imaginary unit powers

PRACTICE PROBLEMS
Solve problems with base i (square root of -1) raised to a positive exponent

### Imaginary roots of negative numbers

VIDEO 4:04 minutes
Imaginary Roots of Negative Numbers

### i as the principal root of -1 (a little technical)

VIDEO 6:44 minutes
i as the principal square root of -1