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.

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

An $n$-th root is primitive iff it is not an $m$-th root of unity for $m \lt n$. If $n$ is a prime number, then all $n$th roots of unity except 1, are primitive.