GATE Complex Analysis: Complex Integration and Residues – Previous Year Questions
11 GATE previous year questions on Complex Integration and Residues (Complex Analysis, Mathematics) with answers and explanations, from every paper.
- GATE 2021 MA Q56 – R=z=x+iy:0<x<1,−11π<y<11π, with positively oriented boundary Γ. Evaluate (2 i)-1 ez/(ez-2)\,dz.
- GATE 2021 MA Q58 – Count the zeros with multiplicity of P(z)=3z⁵+2iz²+7iz+1 in 1< z <7.
- GATE 2022 MA Q14 – Evaluate C z100/(z101+1)\,dz, where C is z =2 counterclockwise.
- GATE 2022 MA Q29 – How many zeros, counting multiplicity, does 2z⁷−7z⁵+2z³−z+1 have in z <1?
- GATE 2023 MA Q15 – On z <1 define f(z)=z-25z3+z5/5!-z7/7!+z9/9!-z11/11!. P:f has three zeros counting multiplicity in the unit disk. Q:f has one zero in 1/2< z <1.…
- GATE 2023 MA Q43 – Let Ω⊆ℂ be open and connected and contain U= z ≤1/2. Let J consist of analytic f on Ω with sup (z,w∈U) f(z)−f(w) =1. P:some f∈J has f′(0) ≥2. Q:every…
- GATE 2024 MA Q12 – C is the ellipse z−2 + z+2 =8 oriented counterclockwise. Evaluate C z2/(z2-2z+2)\,dz.
- GATE 2025 MA Q33 – I=(2 i)-1 C z/[1-(z3)]\,dz, where C is the positively oriented diamond Re z + Im z =1. Find 120I (integer).
- GATE 2025 MA Q63 – Distinct nonzero real α,β and a polynomial Q of degree <5 define f(z)=[6( z)-6(e2 z-Q(z))]/z6. The source says f “satisfies Morera’s theorem in ℂ∖0”.…
- GATE 2026 MA Q38 – Evaluate (1-z)(3 z+5 z)1-z101\,dz, where Γ is z = 7/9, counterclockwise.
- GATE 2026 MA Q59 – Count zeros, with multiplicity, of z6+5z3+4z+11 in 1 < z < 3 (integer).