Holomorphic functions integrate to zero around every closed curve in a simply connected domain.Suggest a slogan
Let \(\Omega\subseteq\CC\) be a simply connected open set, let \(f\) be holomorphic on \(\Omega\), and let \(\gamma\) be a closed piecewise smooth curve in \(\Omega\). Then \[ \int_\gamma f(z)\dz = 0. \]
State the Cauchy-Goursat theorem.