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Locus in complex plane

Source: Czech and Slovak Olympiad 1953, National Round, Problem 1

February 15, 2022
complex numbersPlane

Problem Statement

Find the locus of all numbers z∈Cz\in\mathbb C in complex plane satisfying z+zˉ=a⋅∣z∣,z+\bar z=a\cdot|z|, where a∈Ra\in\mathbb R is given.
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