Compute the contour integral $∫_{|z|=1} \frac{e^{i(1+z)}}{z^{10}}dz$
I am stuck at solving the integral. I know there is a singularity at z=0 and therefore we cannot apply the Cauchy Theorem directly. I used the parametrization $z=e^{it}$ and $dz=ie^{it}$ where $R=1$.
However my integration resulted into a mess and i cannot seem to reach the final answer.