complex analysis question involving Schwarz Lemma: Explain why it is impossible to have an entire function f(z) such that f(0) = 0, |f(z)| ≤ 1000 in the disc |z| < 100 and |f(5 + 12i)| = 131

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 58E
Question

complex analysis question involving Schwarz Lemma:

Explain why it is impossible to have an entire function f(z) such that f(0) = 0, |f(z)| ≤ 1000 in
the disc |z| < 100 and |f(5 + 12i)| = 131.

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