It is given: $c\in \mathbb C, r>0, z_0\notin \partial K_r(c)$ and $n \in \mathbb Z.$
Claculate $\int_{\partial K_r(c)}^{} \! (z-z_0)^{n} \, dz$.
Can someone give me some hint and tell me how to start?
P.S. $\partial K_r(c)$ is a disk (i.e. circle plus its interior) of radius $r$ centered at $c$.
For $n \ne -1$ the integral $=0$, since $(z-z_0)^n $ has an antiderivative
A direct calculation with the definition of a line integral shows that for $n = -1$ the integral = $2 \pi i $