N-th Roots of Unity

The number $n$ that represents the number of solutions for of $z$ for equation $z^n=1$ where:

• $z$ is a Complex Number
• $n$ is an arbitrary Natural Number

The $n$ solutions would be: $\{z_0,z_1\dots z_{n-1}\}$ given by $k\in [0,n-1],z_k=e^{i\frac{2k\pi }{n}}$

Example where $n=3$

Symmetry About the Unit Circle

https://www.youtube.com/watch?v=1BjDKRrR8-E&t=335s