Question Number 124009 by joki last updated on 30/Nov/20
Answered by mindispower last updated on 30/Nov/20
$${f}\left({z}\right)=\frac{{z}^{\mathrm{4}} }{{e}^{{z}} −\mathrm{1}},{is}\:{holomorphic}\:{withe}\:{no}\:{pols}\:{in}\:\Gamma \\ $$$${e}^{{z}} −\mathrm{1}=\mathrm{0}\Rightarrow{z}=\:\mathrm{2}{ik}\pi,{k}\in\mathbb{Z} \\ $$$$\Rightarrow\int_{\Gamma} {f}\left({z}\right){dz}=\mathrm{0} \\ $$