Complex Analysis: Theory and Applications · Problem 1.3.22

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · modulus-difference-squared

Problem

Prove that ∣z1−z2∣2=∣z1∣2−2Re(z1z2‾)+∣z2∣2|z_1 - z_2|^2 = |z_1|^2 - 2\text{Re}(z_1 \overline{z_2}) + |z_2|^2.

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