\begin{definition}[Definition:Contour/Closed/Complex Plane]
Let $C$ be a '''contour''' in $\C$ defined by the (finite) sequence $\left\langle{C_1, \ldots, C_n}\right\rangle$ of directed smooth curves in $\C$.
Let $C_i$ be parameterized by the smooth path $\gamma_i: \left[{a_i \,.\,.\, b_i}\right] \to \C$ for all $i \in \left\{ {1, \ldots, n}\right\}$.
$C$ is a '''closed contour''' {{iff}} the start point of $C$ is equal to the end point of $C$:
:$\gamma_1 \left({a_1}\right) = \gamma_n \left({b_n}\right)$
\end{definition}