Question

How could you describe the location of the roots of unity in the complex plane?

Answer 1

Answer:

They prove to be a set of regular polygons.

Step-by-step explanation:

The roots of unity can be expressed as:

$z_i,_n=\sqrt[n]{1}$

There are n solutions for the n-th root of unity, for $i=0,1,2...,n-1$

All these n solutions are points accross the XY plane, all of them keeping a distance from the center (point $(0,0)$) of 1. They all trace a regular polygon whose circumscribed circumference is of radius 1, too. The number of sides and vertices of this polygon is n.