# 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:

$x^r := \map \exp {r \ln x}$

where $\exp$ denotes the complex exponential function.

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