Question

If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then

• A. $|z|=0$
• B. $|z|=1$
• C. $|z|>0$
• D. $|z|<0$

Answer 1

The correct option is B $|z|=1$

$\frac{z-1}{z+1}$ is purely imaginary
$\frac{z-1}{z+1}=-\frac{\overline{z}-1}{\overline{z}+1}$
$\Rightarrow {\left|z\right|}^2+z-\overline{z}-1=-{\left|z\right|}^2+z+1-\overline{z}$
$\Rightarrow \left|z\right|=1$
Ans: B