Imaginary number

An imaginary number is a complex number whose real part is equal to 0. In the complex plane, these numbers lie on the imaginary axis. They are sometimes also refered to as pure imaginary numbers,

The complex number $z$ is imaginary if and only if $z = i \textrm{Im}(z)$ , where $i = \sqrt{-1}$ is the imaginary unit and $\textrm{Im}$ is the imaginary part function.

The imaginary unit is $i$ , which is $\sqrt{-1}$ . $i$ can be treated as a variable with the distinctive property that $i^2= -1$ . Powers of $i$ can be equal to only 4 possibilities: $-i, i, 1, -1$ because the values cycle. This means that $i^1=i$ , $i^2=-1$ , $i^3=-i$ , $i^4=1$ , $i^5=i....$ .

Multiplying imaginary/complex numbers is not so much different from multiplying variables. In fact, the easiest way to multiply imaginary numbers is to treat $i$ as a variable and then check to see if there is either $i^2$ or $i^4$ in which case you switch it its real value accordingly. [hide="example"] $(2i-1)(i+2)$ $= 2i^2+4i-i-2$ (FOIL) $= 2i^2+3i-2$ $= -2+3i-2$ $= -4+3i$ [/hide]

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Imaginary number

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