Let-a-b-c-complex-numbers-such-that-the-roots-of-the-equation-ax-2-bx-c-0-have-same-modulus-Prove-that-a-0-iff-b-0-

Question Number 125131 by Snail last updated on 03/Jun/21

L e t a, b, c \in c o m p l e x n u m b e r s s u c h t h a t t h e r o o t s

o f t h e e q u a t i o n {a x}^{2} + b x + c = 0 h a v e s a m e m o d u l u s

P r o v e t h a t a = 0 i f f b = 0