Question

State true or false:

The complex numbers $z=x+iy$ which satisfy the equation $\left|\frac{z-5i}{z+5i}\right|=1$ lie on the axis of $Y$.

Answer 1

$\left|\frac{z-5i}{z+5i}\right|=1$ or
${|x+iy-5i|}^2={|x+iy+5i|}^2$
or $x^2+{(y-5)}^2=x^2+{(y+5)}^2$
or $20y=0$ or $y=0$