Q: The complex numbers z = x + iy which satisfy the equation $\large |\frac{z-5i}{z+5i}|$ lie on

(A) the x-axis

(B) the straight line y = 5

(C) a circle passing through the origin

(D) None of these

Sol. $\large |\frac{z-5i}{z+5i}| = 1 $

⇒ |z – 5i| = |z + 5i|

⇒ z would lie on the right bisector of the line segment connecting the points 5i and – 5i . Thus z would lie on the x-axis.

Hence (A) is the correct answer.

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