Imaginary number

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 <math>ib</math> where <math>b</math> is a real number and <math>i</math> the imaginary unit with the property that

<math>i^2 = -1.</math>

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

See also

• Quaternion
• Octonion