In mathematics, an imaginary number is a number whose square is negative. The term was coined by René Descartes in the seventeenth century and was meant to be derogatory: obviously such numbers don't exist. Nowadays we find the imaginary numbers on the vertical axis of the complex number plane. Every imaginary number can be written as where is a real number and the imaginary unit with the property that

(In electrical engineering and related fields, the imaginary unit is often written as to avoid confusion with a changing current, traditionally denoted by .) Every complex number can be written uniquely as a sum of a real number and an imaginary number.

Despite their name, imaginary numbers are just as real as real numbers; see Complex number#Definition on how they can be constructed.

The powers of repeat in a cycle:


See also