A First Course in Complex Analysis · Problem 8.4.12

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis

Problem

Prove Corollary 8.2.6 (Minimum-Modulus Theorem): Suppose ff is holomorphic and nonconstant in a region GG. Then ∣f∣|f| does not attain a weak relative minimum at a point aa in GG unless f(a)=0f(a) = 0.

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