Definition:Root of Unity/Complex

Definition
Let $n \in \Z_{>0}$ be a (strictly) positive integer.

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

Also see

 * Complex Roots of Unity in Exponential Form, where it is shown that $U_n = \set {e^{2 i k \pi / n}: k \in \N_n}$


 * Roots of Unity under Multiplication form Cyclic Group