3. Theorem 2.4.1 - Residue Theorem

Let $U \subseteq C$ be a domain, $f : U - {z_{1}, \dots, z_{k}} \to C$ holomorphic. Suppose $Q \subseteq U$ is a topological disk (image of a disk under a homeomorphism). Suppose $δ Q$ is piecewise $C^{1} (U)$ which does not pass through any $z_{i}$ . Then we have:
:?:

\oint_{δ Q} f (z) d z = 2 π i \sum_{z_{i} \in Q} \underset{z = z_{i}}{R e s} f (z)