GATE 2020 BM – Question 26

Engineering Mathematics · Complex Variables · 1 mark · Numerical answer

Evaluate $\frac1{2\pi j}\oint_C\frac{z}{(z-1)(z-2)}\,dz$ for positively oriented circle $|z|=3/2$.

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Correct answer: -1.1 to -0.9

Explanation

The circle encloses z=1 but not z=2. The residue at one is lim(z−1)f(z)=1/(1−2)=−1. The contour integral is 2πj times this residue; the prefactor cancels 2πj. Therefore the requested value is −1.

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