GATE 2025 IN – Question 33
For $f(z)=\dfrac{2z+1}{z^2-z}$, where $z$ is complex, the sum of residues at its singular points is ______ (in integer).
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Correct answer: 2 to 2
Explanation
The denominator is $z(z-1)$, giving simple poles at 0 and 1.
At 0, $\operatorname{Res}(f,0)=\lim_{z\to0}(2z+1)/(z-1)=-1$.
At 1, $\operatorname{Res}(f,1)=\lim_{z\to1}(2z+1)/z=3$.
The sum is $-1+3=\boxed2$.