i´m preparing my exam on basic complex analysis, and i find out this exercise that i find nice, i need to show that
$ \int_{|z|=1}exp\left(\frac{1}{z^k}\right)=\begin{cases} 2i\pi & k=1\\ 0 & otherwise\\ \end{cases} $ i really don´t know how to deal this problem, i already know the tools but not how to use them, i know that i had Laurent´s series and residue calculus, the problem is that i don´t know how to calculate the residue, can you explain me how to proceed and how to find the residue. Thanks