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Constrained complex equation of three variables

Source: Romanian District Olympiad 2009, Grade X, Problem 2

October 8, 2018
complex numbersabsolute valuealgebra

Problem Statement

Find the complex numbers z1,z2,z3 z_1,z_2,z_3 of same absolute value having the property that: 1=z1z2z3=z1+z2+z3. 1=z_1z_2z_3=z_1+z_2+z_3.
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