A First Course in Complex Analysis · Problem 1.5.25

Complex Numbers — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · reverse-triangle-inequality

Problem

Prove the reverse triangle inequality: for any z1,z2∈Cz_1, z_2 \in \mathbb{C}, ∣±z1±z2∣≥∣∣z1∣−∣z2∣∣.|{\pm z_1 \pm z_2}| \geq \big| |z_1| - |z_2| \big|.

Related theory

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