Let \( a, b, c \) be distinct complex numbers with \( |a|=|b|=|c|=1 \) and \( z_{1}, z_{2} \) be...

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Let \( a, b, c \) be distinct complex numbers with \( |a|=|b|=|c|=1 \) and \( z_{1}, z_{2} \) be the roots of the equation \( a z^{2}+b z+c=0 \) with \( \left|z_{1}\right|=1 \). Also let \( P \) and \( Q \) represents the complex numbers \( z_{1} \) and \( z_{2} \) in the complex plane with \( \angle P O Q=\theta \) where \( O \) is the origin then
(a) \( b^{2}=a c, \theta=\frac{2 \pi}{3} \)
(b) \( \theta=\frac{2 \pi}{3}, P Q=\sqrt{3} \)
(c) \( b^{2}=a c, P Q=2 \sqrt{3} \)
(d) \( 2 b^{2}=a c, \theta=\frac{\pi}{3} \)
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