Question

Let a, b, c be distinct complex numbers with |a| = |b| = |c| = 1 and z₁, z₂ be the roots of the equation az² + bz + c = 0 with |z₁| = 1. Also, let P and Q points represent the complex numbers z₁ and z₂ in the complex plane with ∠POQ = θ where O being the origin. Then 

(A)  b² = ac,  θ = 2π/√3

(B)  θ = 2π/3,PQ = 3

(C)  PQ = 2√3, b² = ac

(A)  θ = π/3,b² = ac

Answer 1

Correct option (A),(B)

Now,  z₂ = z₁e^iθ 

⇒ |z₁ + z₂| = |z₁| |1 + e^iθ