\begin{definition}[Definition:Directed Smooth Curve/Endpoints/Complex Plane]
Let $C$ be a directed smooth curve in the complex plane $\C$.
Let $C$ be parameterized by a smooth path $\gamma: \left[{a \,.\,.\, b}\right] \to \C$.
Then:
: $\gamma \left({a}\right)$ is the '''start point''' of $C$
: $\gamma \left({b}\right)$ is the '''end point''' of $C$.
Collectively, $\gamma \left({a}\right)$ and $\gamma \left({b}\right)$ are known as the '''endpoints''' of $\rho$.
\end{definition}