GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 13 of 65

Marks: +1, -0

The value of the following complex integral, with C representing the unit circle centered at origin in the counter clockwise sense, is:

∫↙{C} \;{z^{2}+1}/{z^{2}-2 z} d z

Solution:

∮↙{c} \;{(z^{2}+1)}/{z(z-2)} d z

∮↙{c} \;{(z+1)}/{z(z-2)}=2 π i(Re(z=0)]

= \;\; 2 π i[\;{0+1}/{0-2}]

= \;\; 2 π i[-\;{1}/{2}]=-π i

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