The GATE Grind

GATE Complex Analysis: Conformal Mappings – Previous Year Questions

5 GATE previous year questions on Conformal Mappings (Complex Analysis, Mathematics) with answers and explanations, from every paper.

  1. GATE 2021 MA Q13 (1 mark, Multiple choice) – A Möbius map T(z)=(az+b)/(cz+d),ad−bc≠0, sends 0,−i,∞ to 10,5−5i,5+5i respectively. Find T(Re z<0).
  2. GATE 2022 MA Q50 (2 marks, Multiple select) – A Möbius T satisfies T(0)=α,T(α)=0,T(∞)=−α, where α=(−1+i)/√2. L is the line through zero of slope −1; C is the unit circle. Which hold?
  3. GATE 2025 MA Q41 (2 marks, Multiple choice) – A Möbius transformation sends 0,1/2,1 to −3,∞,2. It maps the circle centered at 1 with radius k to line αx+βy+γ=0. Find [2k(α+β)+γ]/[α+β−2kγ].
  4. GATE 2025 MA Q42 (2 marks, Multiple choice) – Let U=Im z>0, D= z <1. Over all bijective analytic f:U→D with f(i)=0, find sup f(4i) .
  5. GATE 2026 MA Q50 (2 marks, Multiple select) – On D = z <1, set f(z)=z/(1-z) and g(z)=(1+z)/(1-z). S₁: f(D)⊆g(D); S₂: g(D)⊆f(D). Which statements hold?