Imaginary Number

Colorized Definition

imaginary number


\forward 1 \plain \cdot \sideways i^2 &= \backward -1 \
\sideways i &= \halfway \sqrt{ \backward -1 }

\forward Facing forward, \sideways two 90-degree rotations \plain is \backward backward. \

\sideways An imaginary number \plain is \halfway halfway \backward backward.

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.

## Read More - [A visual, intuitive guide to imaginary numbers](