Question

The complex number z which satisfies the condition $\left|\frac{i+z}{i-z}\right|=1$ lies on

• A. circle $x^2+y^2=1$
• B. the x-axis
• C. the y-axis
• D. the line x + y =1

Answer 1

The correct option is A

circle $x^2+y^2=1$

Given that, $\left|\frac{i+z}{i-z}\right|=1$

Let z = x + iy

$\therefore \left|\frac{x+i(y+1)}{-x-(y-1)}\right|=1\Rightarrow \frac{x^2+(y+1{)}^2}{x^2+(y-1{)}^2}=1\Rightarrow x^2+(y+1{)}^2=x^2+(y-1{)}^2\Rightarrow 4y=0\Rightarrow y=0$

So, z lies on X-axis (real axis).