Question

If z is a complex number such that $\left|\frac{z-3i}{z+3i}\right|=1$ then z lies on?

• A. The real axis
• B. The line Im(z)$=3$
• C. A circle
• D. None of these

Answer 1

The correct option is A The real axis

Given $\left|\frac{z-3i}{z+3i}\right|=1$

$\Rightarrow \left|\frac{z-3i}{z+3i}\right|=1$

$\Rightarrow z$ is equidistant from $(0,3)$ & $(0,-3)$

It lies on real axis.