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