GATE Mathematical Physics: complex analysis: Cauchy-Riemann conditions, Cauchy's theorem, singularities, residue theorem and applications – Previous Year Questions

7 GATE previous year questions on complex analysis: Cauchy-Riemann conditions, Cauchy's theorem, singularities, residue theorem and applications (Mathematical Physics, Physics) with answers and explanations, from every paper.

1. GATE 2022 PH Q25 (1 mark, Multiple select) – For real a, f(z)=z+ z-a 2 is
2. GATE 2023 PH Q43 (2 marks, Multiple choice) – U=xy(x2-y2) and V=ax4+by4+cx2y2+k. If U+iV is analytic, find abc.
3. GATE 2023 PH Q56 (2 marks, Multiple select) – For f(z)=z2 z/(z-)4, which statements at z= are correct?
4. GATE 2026 PH Q36 (2 marks, Multiple choice) – The function f(z) of complex variable z given below, f(z)=z2-5z+4z3+4z-z2-4, has singular points at z=
5. GATE 2025 PH Q21 (1 mark, Multiple choice) – Consider f(z)=1/[z2(z-2)3] of a complex variable z. The residues at z=0 and z=2, respectively, are
6. GATE 2025 PH Q55 (2 marks, Multiple select) – Consider I=12 iz4-1(z-a/b)(z-b/a)\,dz, on the unit circle centered at the origin, where a,b>0. Which option(s) is/are correct?
7. GATE 2024 PH Q31 (1 mark, Multiple select) – The complex function e-2/(z-1) has