Complex numbers are an extension to the number space providing solutions for square roots of negative numbers.

The basic constant of complex numbers is **i** which is defined as solution of sqrt(-1).

If real numbers are thought as a line of infinite length, then the **imaginary numbers** (multiples of **i**) are on a line by the location of 0 on real numbers' line, rotated by pi/4 (or 90 degrees). Both lines define a **plane** of complex numbers. A complex number can hence be imagined as a pair of

{real imaginary}

components.

DKF: They can also be described using "polar coordinates" (i.e. angle and magnitude) which is a format that makes multiplication, division, exponentiation and (simple) root-finding much simpler.

See also