This is a contour integral from a proof, somebody there told me it followed from cauchy integral formula, i know (i probably dont understand it) cauchys integral formula: $f(z_0)=\frac{1}{2\pi i}\int_\gamma \frac{f(z)}{z-z_0}$and i dont understand how one can get to this :
$\int_\gamma \frac{1}{2z}dz =\pi i$
with the help of it. Please do tell me if you see it.