Definition:Root of Unity/Complex

Definition
The complex $n$th roots of unity are the elements of the set:
 * $U_n = \left\{{z \in \C: z^n = 1}\right\}$

Also see
Roots of Unity, where it is shown that:
 * $U_n = \left\{{e^{2 i k \pi / n}: k \in \N_n}\right\}$

If $e^{2 i k \pi / n} =: \omega$, then $U_n$ can be written as:
 * $U_n = \left\{{1, \omega, \omega^2, \ldots, \omega^{n-1}}\right\}$