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Set of complex numbers given by inequality

Source: Czech and Slovak Olympiad 1969, National Round, Problem 4

July 3, 2024
complex numbersalgebraabsolute valueinequalities

Problem Statement

Determine all complex numbers zz such that ∣z−∣z+∣z∣∣∣−∣z∣3≥0\Bigl|z-\bigl|z+|z|\bigr|\Bigr|-|z|\sqrt3\ge0 and draw the set of all such zz in complex plane.
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