Complex Analysis: Theory and Applications · Problem 1.3.17

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · modulus-difference-identity

Problem

Suppose that either ∣z∣=1|z| = 1 or ∣w∣=1|w| = 1. Prove that ∣z−w∣=∣1−z‾w∣|z - w| = |1 - \overline{z}w|.

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