Aleph Zero Home

A complex number can be raised to a power, which need not be a whole number. So, for example, raising z to the power 1/2 will give the square root of z.

The easiest way to do this is to express the complex number in polar form, z = re^iθ.

To raise the number z = re^iθ to power p we have,
z^p = r^pe^ip*θ

That is we raise the modulus to the power p, and multiply the argument by p.

We can then convert back from polar form as described here.