Question Number 37307 by math khazana by abdo last updated on 11/Jun/18
$${calculate}\:\:\:\int_{\gamma} \:\:\:\:\frac{{dz}}{{z}}\:\:\:{with}\:\gamma\:=\left\{{z}\in{C}\:/\mid{z}\mid=\mathrm{1}\right\}\:. \\ $$
Commented by prof Abdo imad last updated on 15/Jun/18
$${o}\:\:{is}\:{pole}\:{of}\:{f}\left({z}\right)=\frac{\mathrm{1}}{{z}}\:\Rightarrow \\ $$$$\int_{\gamma} {f}\left({z}\right){dz}=\mathrm{2}{i}\pi{Re}\left({f},\mathrm{0}\right)\:=\mathrm{2}{i}\pi\:. \\ $$