Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Complex Analysis Calculus of Residues
Residue of \(f(z)=\frac{\log (1+z)}{\left(1+z^{2}\right)^{2}}\) at z = i is given by
1
\(\frac{1}{8}-\frac{\pi}{16}+i\left[-\frac{1}{8}+\frac{1}{4} \log \sqrt{2}\right]\)
2
\(-\frac{1}{8}+\frac{\pi}{16}+i\left[\frac{1}{8}-\frac{1}{4} \log \sqrt{2}\right]\)
3
\(-\frac{1}{8}+\frac{\pi}{16}+i\left[-\frac{1}{8}+\frac{1}{4} \log \sqrt{2}\right]\)
4
\(\frac{1}{8}-\frac{\pi}{16}+i\left[\frac{1}{8}-\frac{1}{4} \log \sqrt{2}\right]\)
5
Question Not Attempted