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Complex modulus property

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December 14, 2019
complex numbersalgebra

Problem Statement

Let be three nonzero complex numbers a,b,c a,b,c satisfying ∣a∣=∣b∣=∣c∣=∣a+b+c−abcab+bc+ca−1∣. |a|=|b|=|c|=\left| \frac{a+b+c-abc}{ab+bc+ca-1} \right| . Prove that these three numbers have all modulus 1 1 or there are two distinct numbers among them whose sum is 0. 0.
Costel Anghel
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