Question

Let z₁ and z₂ be two complex numbers such that arg (z₁ – z₂) = π/4 and z₁,z₂ satisfy the equation |z – 3| = Re(z). Then the imaginary part of z₁ + z₂ is equal to _________.

Answer 1

|z – 3| = Re(z)

let Z = x = iy

⇒ (x-3)² + y² = x² 

⇒ x² + 9 – 6x + y² = x² 

⇒ y² = 6x-9

⇒ y² = 6(x-\(\frac{3}{2}\))

⇒ z₁ and z₂ lie on the parabola mentioned in eq.(1)

= 6.00

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