Winding number

Let \(\gamma\) be a closed piecewise \(C^1\) curve in \(\CC\) and let \(z_0\in\CC\) be a point not on \(\gamma\). The winding number, or index, of \(\gamma\) about \(z_0\) is \[ n(\gamma, z_0)\coloneqq\frac{1}{2\pi i}\int_\gamma\frac{1}{\xi-z_0}\dxi. \]