Question

If \( z_{1}-z_{2} \) are two complex numbers such that \( \left|\frac{z_{1}}{z_{2}}\right|=1 \) and \( \arg \left(z_{1} z_{2}\right)=0 \), then (A) \( z_{1}=z_{2} \) (B) \( \left|z_{2}\right|^{2}=z_{1} z_{2} \) (C) \( z_{1} z_{2}=1 \) (D) none of these

Answer 1

From the first equation, |z₁|=|z₂|

From the second equation, arg(z₁)+arg(z₂)=0, the complex numbers are conjugate of each other.

So |z₁|²=|z₂|²=z₁z₂=Re²(z)+Im(z)². Option (B) is correct!!