I am asked this question :
Let $f(z)=a_0+a_1z+...+a_nz^n$ be a complex polynomial with complex coefficients. Prove that :
$$\frac{1}{2\pi i}\oint\limits_{|z|=r}z^{n-1}|f(z)|^2\mathrm{dz}=a_0a_n^*r^{2n}$$
I have tried pretty much everything and I am still lost. I am pretty sure that Cauchy's Theorem gets the job done but I didn't have any luck yet.
