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

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

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

Where .

The all roots are placed on a circle.

The roots are equally spaced means the angle between any consecutive roots is same.

Find the angle between the roots and .

The angle of root is .

The angle of root is .

.

Find the angle between the roots and .

The angle of root is .

The angle of root is .

.

The angle between , and , are same.

Therefore, the roots are equally szpaced.

Hence the theorem is proved.

Therom is proved.