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


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

$L e t a, b, c \in c o m p l e x n u m b e r s s u c h t h a t t h e r o o t s$ $o f t h e e q u a t i o n {a x}^{2} + b x + c = 0 h a v e s a m e m o d u l u s$ $P r o v e t h a t a = 0 i f f b = 0$
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