\begin{definition}[Definition:Power (Algebra)/Complex Number]
Let $z, k \in \C$ be any complex numbers.
'''$z$ to the power of $k$''' is defined as the multifunction:
:$z^k := e^{k \ln \paren z}$
where $e^z$ is the exponential function and $\ln$ is the  natural logarithm multifunction.
\end{definition}