# Imaginary Number

## Colorized Definition

## Plain English

**What's an imaginary number?** A number pointing sideways (North/South) isntead of the typical East/West number line. ("Imaginary" was a derogatory name from critics, Gauss wanted them called "lateral" numbers.)

**What does i mean?** i, by itself, points North. Multiplying by i rotates you 90 degrees. 2 rotations points you backwards (i * i = -1), 4 rotations spins you around fully (i^4 = 1).

**Is i useful?** The second dimension is useful, right? Imaginary numbers make 2d rotation problems simple.

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