The GATE Grind

GATE Complex Analysis: Power Series and Singularities – Previous Year Questions

4 GATE previous year questions on Power Series and Singularities (Complex Analysis, Mathematics) with answers and explanations, from every paper.

  1. GATE 2021 MA Q57 (2 marks, Numerical answer) – On z <2π, f(z)=3z²/(1−cos z) for z≠0 and f(0)=6. If f=Σₙ₌₀∞a nzⁿ, find 6a₂.
  2. GATE 2022 MA Q28 (1 mark, Numerical answer) – Find the radius of convergence of n03n+1z2n to two decimals.
  3. GATE 2023 MA Q27 (1 mark, Numerical answer) – Near zero, z/(1-z-z2)= n=0 a nzn. Find a₆+a₅.
  4. GATE 2026 MA Q35 (1 mark, Numerical answer) – The series n=0 a n(z-2)n converges at z = 5 and diverges at z = −1. Find its radius of convergence (integer).