Chapter 14.5, Problem 1P

If $C$ is a circle of radius $\rho$ about $z_0,$ show that ${\displaystyle {\oint }_C\frac{dz}{{\left(z-z_0\right)}^n}}=2\pi i\text{ if }n=1$ but for any other integral value of n, positive or negative, the integral is zero. Hint:

Use the fact that $z=z_0+\rho e^{i\theta }$ on $C$.