Imaginary number
From Wikinfo
[[es:N�mero imaginario]]
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 <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.
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
References
- Adapted from the Wikipedia article, "Imaginary_number" http://en.wikipedia.org/wiki/Imaginary_number, used under the GNU Free Documentation License
