GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 30 of 65

Marks: +1, -0

The value of the integral in counter clockwise direction around a circle

{C}

of radius 1 with center at the point

z=-2

Solution:

∫ \;{z+1}/{z^{2}-4} d z

∫ \;{z+1}/{(z-2)(z+2)} d z

∫ \;{({z+1}/{z-2})}/{(z+2)} d z

where,

f(z)=\;{z+1}/{z-2}

=2 π i f(-2)

=2 π i(\;{-2+1}/{-2-2})

=2 π i(\;{-1}/{-4})=\;{π i}/{2}

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