A First Course in Complex Analysis · Problem 2.5.5

Differentiation — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · limits-complex-functions

Problem

Suppose lim⁡z→z0∣f(z)∣=0\lim_{z \to z_0} |f(z)| = 0. Show that lim⁡z→z0f(z)=0\lim_{z \to z_0} f(z) = 0.

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