Part BCSIR NET December 2024room-inside-the-domain-shrinks-the-derivative

Room inside the domain shrinks the derivative

Let ℍ = {z = x + iy $\in C$ | y > 0} and f : ℍ $\to C$ be a non-constant holomorphic function satisfying |f(z)| < 1 for all z ∈ ℍ. Which of the following statements is true?

A. $lim (y \to + \infty) f^{'} ($ iy) = 0✓
B. $lim (y \to + \infty) f^{'} ($ iy) is a complex number with absolute value 1.
C. $lim (y \to + \infty)$ |f′(iy)| $= + \infty$
D. $lim (y \to + \infty) f^{'} ($ iy) is not a real number.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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Room inside the domain shrinks the derivative

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