Answer to Question #223822 in Chemical Engineering for Lokika

Question

The residue at z=1 of the function 2z/(1-z)(z+1)

Answer 1

The residue at z= 1 is

$\lim _{z\to \:1}\left(\left(z-1\right)\frac{2z}{\left(1-z\right)\left(z+1\right)}\right)\\ =-\frac{2z}{z+1}\\ =\lim _{z\to \:1}\left(-\frac{2z}{z+1}\right)\\ \mathrm{Plug\:in\:the\:value}\:z=1\\ =-\frac{2\cdot \:1}{1+1}\\ =-1$