Complex numbers

Complex numbers provides a system for

1. manipulating rotating vectors, and
2. representing geometric effects of common digital signal processing operations (e.g. filtering), in algebraic form.

In rectangular (or Cartesian) form, the complex number $z$ is defined by the notation

$$z = x + jy.$$

The part without the $j$ is called the real part, and the part with the $j$ is called the imaginary part.