Definition:Power (Algebra)/Complex Number

Definition
Let $z, k \in \C$ be any complex numbers.

Then we define the $z$ to the power of $k$ to be:


 * $z^k := e^{k \operatorname{Log} \left({z}\right)}$

where $e^x$ is the exponential function and $\operatorname{Log}$ is the principal branch of the natural logarithm function.