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General complex inequality

Source: G.M.

November 25, 2019
inequalitiesalgebracomplex numbers

Problem Statement

Prove the complex inequality ∣x∣+∣y∣+∣z∣≤∣x+y+z∣+∣x−z∣+∣z−y∣+∣y−z∣. |x|+|y|+|z|\le |x+y+z| +|x-z| +|z-y|+|y-z|.
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