GATE Complex Analysis: Analytic and Harmonic Functions – Previous Year Questions
10 GATE previous year questions on Analytic and Harmonic Functions (Complex Analysis, Mathematics) with answers and explanations, from every paper.
- GATE 2021 MA Q12 – A nonconstant entire f(z)=u(x,y)+iv(x,y),z=x+iy, defines g₁=u x−iu y and g₂=v x+iv y. Which holds?
- GATE 2022 MA Q13 – Let u=e2x[3x2y3y-3x2y3y]. Its harmonic conjugate v satisfies v(0,0)=2. For z=x+iy and f=u+iv, find 4+2if(iπ).
- GATE 2023 MA Q42 – On the unit disk f(z)=Σₙ₌₀∞a nzⁿ, where a₀=a₁=1 and a n=1/2(2n) for n≥2. P:f is one-to-one in some neighborhood of every disk point. Q:f( z ≤1/2) is…
- GATE 2024 MA Q11 – An entire f satisfies f(z) =1 whenever Im z=0. Which statement is correct?
- GATE 2024 MA Q36 – D is the unit disk, H the upper half-plane. Over analytic f:D→H with f(0)=i/2, find sup f′(0) .
- GATE 2024 MA Q37 – On z =1, which function is a uniform limit of polynomials in z?
- GATE 2025 MA Q43 – On a nonempty connected open Ω⊂ℂ, f is nonconstant. S1: if f is continuous and f² analytic, f is analytic. S2: if f² and f³ are analytic, f is…
- GATE 2026 MA Q17 – f: C C is f(z)= z 2-5 z+2. At which listed point is f complex differentiable?
- GATE 2026 MA Q18 – Let D = z ∈ ℂ: z < 1. An analytic map f:D→D has f(0) = 0. Which is a possible f′(0)?
- GATE 2026 MA Q39 – On which domain does f(z)= n=15-n(nz) represent an analytic function?