Definition:Power (Algebra)/Real Number/Complex

Definition
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:


 * $x^r := \exp \left({r \ln x}\right)$

where $\exp$ denotes the complex exponential function.

When $x = e$ this reduces to the definition of the complex exponential function.