Question

If $z_1,z_2$ be two non zero complex numbers satisfying the equation $\left|\frac{z_1+z_2}{z_1-z_2}\right|=1$ then $\frac{z_1}{z_2}+\left(\frac{z_1}{z_2}\right)$ is

• A. zero
• B. 1
• C. purely imaginary
• D. 2

Answer 1

The correct option is A zero

let $\frac{z_1}{z_2}=x$

given $|\frac{x+1}{x-1}|=1$

$\Rightarrow |x+1|=|x-1|$

Let $x=a+ib$

We get $|a+1+ib|=|a-1+ib|$

$\Rightarrow a=0$

Therefore $x=ib$ and $\overline{x}=-ib$

Therefore $x+\overline{x}=ib-ib=0$

So the correct option is $A$