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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 |
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Answer» 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!! |
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