Question

The complex number $z=x+iy$ which satisfies the equation $\left|\frac{z-7i}{z+7i}\right|=1$ lies on

• A. x-axis
• B. y-axis
• C. on a circle
• D. the line $y=7$

Answer 1

The correct option is A x-axis

Simplifying, we get
$|z-7i|=|z+7i|$
Let $z=x+iy$
Hence,
$(x{)}^2+(y-7{)}^2=x^2+(y+7{)}^2$
$(y+7{)}^2-(y-7{)}^2=0$
$28y=0$
$y=0$
Therefore, $z$ lies on $x$ axis. Hence $z$ is purely real.