Let $U \subseteq \mathbb{C}$ be a D5008: Standard open complex set such that
| (i) | $f : U \to \mathbb{C}$ is a D1392: Holomorphic function on $U$ |
| (ii) | $C \subseteq \mathbb{C}$ is a D1403: Euclidean circle |
| (iii) | \begin{equation} \text{int}(C) \subseteq U \end{equation} |
Then
\begin{equation}
\int_C f(z) \, d z
= 0
\end{equation}