Definition:Root of Unity

Definition
Let $n \in \Z$ be an integer such that $n > 0$.

Let $F$ be a field.

The $n$th roots of unity of $F$ are defined as:


 * $U_n = \left\{{z \in F: z^n = 1}\right\}$

From Roots of Unity we have that when $F = \C$:
 * $U_n = \left\{{e^{2 i k \pi / n}: k \in \N_n}\right\}$

Primitive Root of Unity
A primitive $n^\text{th}$ root of unity of $F$ is an element $\alpha \in U_n$ such that:


 * $U_n = \{ 1,\alpha, \ldots, \alpha^{n-1} \}$