Complex Analysis: Theory and Applications · Problem 3.2.14

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · analytic-zero-real-part-constant

Problem

Let ff be an analytic function in the domain DD. Show that if Re[f(z)]=0\mathrm{Re}[f(z)] = 0 at all points in DD, then ff is constant in DD.

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