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

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

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