Cauchy-Goursat Theorem

Let $f$ be analytic in a simply connected domain $D$. If $C$ is a simple closed contour lying in $D$,

Deformation Invariance Theorem

Let $C_1$ and $C_2$ be 2 positively oriented simple closed contours, with $C_2$ lying inside the interior of $C_1$. Let $f$ be analytic in a domain $D$ that contains both $C_1$ and $C_2$, together with the region between them.

Key Integral

Let $z_0$ be a fixed complex number, and let $C$ be a simple closed contour with positive orientation such that $z_0$ lies inside $C$.