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, if and only if $C$ is positively oriented with respect to $\Int C$.

$C$ is negatively oriented, if and only if $C$ 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.

$\blacksquare$