Roots of Unity

$n$-th roots of unity ($1$) are the complex numbers that satisfy the equation, $z^n = 1$. There are $n$ distinct solutions.

$$z = \exp\bigg({i\Big(\frac{2m\pi}{n}\Big)}\bigg) \;\; \text{where} \;\; m\in \mathbb{Z}\cup[0,n)$$

The solution can be written as $1, w, w^2, w^3, \dots, w^{n-1}$. $$

$1$ is called the trivial solution. Other solutions are called as primitive $n$-th roots.