Project proposal: Complex numbers

Complex numbers (and quaternions, and \(e^{- \pi i}\))

Numbers are the first thing people think of when they think of math, but complex numbers are where it gets really interesting. There are all sorts of cool applications, and the scope is pretty narrow and easily defined. Why not make them the focus of our first project?

The purpose of this page is to sketch out what a Complex Numbers project might look like, so we can evaluate whether it would make a good project.

Goal of the project

• Provide a guide to complex numbers that would be enlightening to Math 1-3 readers.

Outline

1. Basic intro—provide quick intuitive definitions for each math level, including an explanation of \(i\)

• Complex numbers are necessary to solve quadratic equation

• Operations you can do with complex numbers

• Polar form

• Euler’s formula

1. Additional concepts

• Complex plane (graphic complex numbers)

• Set of all complex numbers: \(\mathbb C\)

• Fractals

• Quaternion

1. Exercises to test of understanding of each type of number.