Question

If $\left|\frac{z_1}{z_2}\right|=1$ and $\arg \left(z_1{z}_2\right)=0$, then

• A. $z_1=z_2$
• B. $|z_2{|}^2=z_1{z}_2$
• C. $z_1{z}_2=1$
• D. $z_1=2z_2$

Answer 1

The correct option is B $|z_2{|}^2=z_1{z}_2$

Given that $\arg \left(z_1{z}_2\right)=0$
So, let $z_1{z}_2=k,(k>0)$
$\Rightarrow |z_1{z}_2|=k$
$\Rightarrow |z_1||z_2|=k$
$\because \left|\frac{z_1}{z_2}\right|=1\Rightarrow \left|z_1\right|=\left|z_2\right|$
$\Rightarrow |z_2||z_2|=k$
$\because k=z_1{z}_2$
$\therefore |z_2{|}^2=z_1{z}_2$