\begin{definition}[Definition:Power (Algebra)/Real Number/Complex]
Let $x \in \R$ be a real number such that $x > 0$.
Let $r \in \C$ be ''any'' complex number.
Then we define $x^r$ as:
:$x^r := \map \exp {r \ln x}$
where $\exp$ denotes the complex exponential function.
When $x = e$ this reduces to the definition of the complex exponential function.
\end{definition}