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

*ib* where

*b* is a

real number and

*i* the

**imaginary unit** with the property that

*i*^{2} = -1. (In

electrical engineering and related fields, the imaginary unit is often written as

*j* to avoid confusion with a changing

current, traditionally denoted by

*i*.) Every complex number can be written uniquely as a sum of a real number and an imaginary number.