Complex representation of a pentagon
Source: Romanian National Olympiad 2003, grade x, p.2
August 27, 2019
complex numbersabsolute valuealgebrageometrypentagon
Problem Statement
Let be five nonzero complex numbers having the same absolute value and such that zero is equal to their sum, which is equal to the sum of their squares. Prove that the affixes of these numbers in the complex plane form a regular pentagon.
Daniel Jinga