Each complex root of a nonzero complex number has the same magnitude.

Let , be a complex number and let be an integer.

If , there are distinct complex roots of given by the formula:

Where .

We will not prove this result in its entirety.

Instead,we shall show only that each in the equation satisfies the equation

proving that each is a complex root of .

Apply De Moivres therom:

So for each , is a complex root of .

Therefore each complex root of a nonzero complex number has the same magnitude.

The Therom is proved.