View source

<!--  via Wikipedia: Imaginary number
    
      last updated: 2003-12-19T17:55:56Z
      updated by: Bcorr
      update comment: Reverted to last edit by Alex S
      
//-->

[[es:N�mero imaginario]] [[ja:&#34394;&#25968;&#21336;&#20301;]]
[[pl:Liczby urojone]]

In [[mathematics]], an '''imaginary number''' is a number whose square is negative. The term was coined by [[Rene Descartes|Ren&eacute; 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 (electricity)|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.

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 <math>i</math> repeat in a cycle:

:<math>i^1 = i</math>
:<math>i^2 = -1</math>
:<math>i^3 = -i</math>
:<math>i^4 = 1</math>
:<math>i^5 = i</math>
:<math>i^6 = -1</math>...

==See also== 
*[[Quaternion]] 
*[[Octonion]]

<!--  NOTE TO EDITORS: 
Per the GNU Free Documentation License, please include the live link below to the adapted Wikipedia article:
//-->

====References====
* Adapted from the [[Wikipedia]] article, "Imaginary_number" [http://en.wikipedia.org/wiki/Imaginary_number http://en.wikipedia.org/wiki/Imaginary_number], used under the [[GNU Free Documentation License]]