\begin{definition}[Definition:Power (Algebra)/Complex Number/Principal Branch/Positive Real Base]
Let $t > 0$ be a real number and let $k$ be a complex number.
The principal branch of a positive real number raised to a complex power is defined as:
:$t^k = e^{k \ln t}$
where $\ln$ is the natural logarithm of a positive real number.
Category:Definitions/Complex Powers
\end{definition}