Question #223822

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

Expert's answer

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

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