Imaginary number

In mathematics, an imaginary number is a number whose square is negative. 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.

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 $i$ repeat in a cycle:

$i^{1}=i$

$i^{2}=-1$

$i^{3}=-i$

$i^{4}=1$

$i^{5}=i$

<Kurtis is a sphincter>i^6 = i</math>

$i^{7}=-1$...

See also

• Quaternion
• Octonion