Hello,

I had an assignment that required me to solve for the roots of unity for various equations of the form . Then , I was asked to represent the roots of unity for each equation on an argand diagram in the form of a regular polygon.

I did all of that , however, i have a question:

is there a relation ship between the power n and the length from one root to the other roots?

When n = 3,

The roots are and 1. The length from one root to the other roots are both 1.7321 (sqrt of 3)

When n = 4,

The roots are . The length from one root to the other roots are (sqrt 2, sqrt and 2)

I am wondering , for the equation , is there a formula relating the power of z to the length from one roots to the other roots?

Thanks.