Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Complex Analysis Calculus of Residues
Consider the function f(z) = (1 + z2)-2 log(1 + z) then Res [f(z); -i] is
1
\( {\left[\frac{\pi}{6}+\frac{1}{8}\right]-i\left[\frac{1}{2}+\frac{\sqrt{2}}{4}\right]} \)
2
\( {\left[-\frac{1}{8}+\frac{\pi}{16}\right]+i\left[-\frac{1}{8}+\frac{\ln \sqrt{2}}{4}\right]} \)
3
\(-\left[\frac{1}{8}+\frac{2 \pi}{21}\right]-i\left[-\frac{1}{8}+\frac{\ln \sqrt{2}}{8}\right] \)
4
None of these.
5
Question Not Attempted