# Complex Numbers 101

A complex number *x*+*y*i has two parts: a *real* part *x* and an *imaginary* part. The symbol i denotes the square root of -1. For purposes of this game, you can think of *x* and *y* as coordinates on a 2D plane, like this:

This is called the ``complex plane''. A complex number can also be represented by polar coordinates, like this:

The *magnitude* is the distance from the origin. The *phase* is the angle with the positive real axis.

In the game, your ``self'' is a point in the complex plane. The Fourier Transform converts this point to a wave pattern of complex numbers, displayed as colors. The ``Radar'' portion of the display shows the color of the numbers in the complex plane. For example, in the default ``complex'' coloring, the phase is shown by color, and the magnitude by brightness. In the ``magnitude'' coloring (grey), the numbers are colored shades of grey based solely on their magnitudes.

The angular sweep-and-fade of the radar is for show only. The coloring within the Fourier portion of the display does not fade likewise.

Back to "Radar"