Holomorphic functions have zero integral around every closed curve in a simply connected region.Suggest a slogan
Let \(\Omega\subseteq\CC\) be a simply connected region and let \(f\) be holomorphic on \(\Omega\). Then for every closed piecewise \(C^1\) curve \(\gamma\) in \(\Omega\), \[ \int_\gamma f(z)\dz=0. \]