Imaginary Unit to Power of Itself/Complete

Theorem

 * $i^i = \set {\exp \paren {\dfrac {4 k + 3} 2 \pi}: k \in \Z}$

where $i$ is the imaginary unit.

Also presented as
This result can also be presented as:


 * $i^i = \set {\exp \paren {- \dfrac \pi 2 \paren {4 k + 1} }: k \in \Z}$