Cauchy-Goursat Theorem

Theorem
Let $f: D \to \C$ be a holomorphic function, where $D \subseteq \C$ is a simply connected domain.

Let $C$ be a closed contour in $D$.

Then:


 * $\ds \oint_C \map f z \rd z = 0$

Also known as
This result is also known as Cauchy's Integral Theorem or the Cauchy Integral Theorem.