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evaluate cyclic integration of[ 3*(z)square +7z+1]dz\z+1,where c is a circle and b=mode of z+i=1,solve by using residue

evaluate  cyclic integration of[ 3*(z)square +7z+1]dz\z+1,where c is a circle and b=mode of z+i=1,solve by using residue

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
I = \oint \frac{3z^{2}+7z+1}{z+1}dz
I = \oint \frac{3z^{2}+7z+1}{(z-(-1)^{1}}dz
I = 2\pi i Residue (z=-1)f(z)
Residue (z=-1)f(z) = 3z^{2}+7z+1|_{z = -1}
Residue (z=-1)f(z) = 3(-1)^{2}+7(-1)+1 = -3
I = -6\pi i
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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