Definition:Periodic Function/Complex

Definition
Let $f: \C \to \C$ be a complex function.

Then $f$ is periodic :
 * $\exists L \in \C_{\ne 0}: \forall x \in \C: f \left({x}\right) = f \left({x + L}\right)$

Also see

 * General Periodicity Property: after every distance $L$, the function $f$ repeats itself.