GATE 2026 MA – Question 18

Complex Analysis · Analytic and Harmonic Functions · 1 mark · Multiple choice

Let D = {z ∈ ℂ: |z| < 1}. An analytic map f:D→D has f(0) = 0. Which is a possible f′(0)?

Show answer and explanation

Correct answer: (B) $i/10$

Explanation

Schwarz’s lemma bounds |f′(0)| ≤ 1. Only i/10 has modulus at most one, and f(z) = iz/10 explicitly realizes it. **B**.

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