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.