Question
Given \(f(z)=\frac{1}{z+1}-\frac{2}{z+3}\). If C is a counterclockwise path in the z-plane such that |z + 1| = 1, the value of \(\frac{1}{2\pi i}\int_c f(z)dz\) is
The correct answer is
1
The circle is centred at−1 with radius1. It encloses the pole at−1, residue1, and excludes−3. Dividing the counterclockwise contour integral by2πi therefore gives 1.
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Important Questions from Complex Variables
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