MathDB

4

Part of 1969 Czech and Slovak Olympiad III A

Problems(1)

Set of complex numbers given by inequality

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

7/3/2024
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.
complex numbersalgebraabsolute valueinequalities