Question

If $\frac{z-1}{z+1}$ is purely imaginary then $|z|$=

• A. 1
• B. 0
• C. -1
• D. 2

Answer 1

The correct option is A 1

if $\frac{z-1}{z+1}$ is purely imaginary

Then $\frac{z-1}{z+1}+\frac{\overline{z}-1}{\overline{z}+1}=0$

(Sum of purely imaginary complex number and its conjugate is equal to 0)

$\Rightarrow |z{|}^2+z-\overline{z}-1+|z{|}^2-z+\overline{z}-1=0$

$\Rightarrow |z|=1$