Reversed Contour Reverses Orientation/Corollary

Corollary
Let $C$ be a simple closed contour in the complex plane $\C$. Let $-C$ be the reversed contour of $C$.

If $C$ is positively oriented, then $-C$ is negatively oriented.

If $C$ is negatively oriented, then $-C$ is positively oriented.

Proof
From Orientation of Simple Closed Contour is with Respect to Interior, it follows that:


 * $C$ is positively oriented, $C$ is positively oriented with respect to $\Int C$.


 * $C$ is negatively oriented, $C$ is negatively oriented with respect to $\Int C$.

where $\Int C$ denotes the interior of $C$.

The claims of the corollary now follow from the main theorem Reversed Contour Reverses Orientation.