Let \( a, b, c \) be distinct non zero complex numbers with \( |a|= \) \( |b|=|c| \) if each of ...

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Let \( a, b, c \) be distinct non zero complex numbers with \( |a|= \) \( |b|=|c| \) if each of equations \( a z^{2}+b z+c=0 \) and \( b z^{2}+c z+ \) \( a=0 \) has a root having modulus 1 , then
(a) \( b^{2}=a c \)
(b) \( c^{2}=a b \)
(c) \( |a-b|=|b-c|=|c-a| \)
(d) \( a^{2}=b c \)
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