Question

If |z -5i| / |z+5i| = 1. Prove that complex number z lie on x-asis.

Answer 1

⇒ |x + i(y - 5)| = |x + i(y + 5)|

⇒ x2 + (y - 5)2 = x2 + (y + 5)2

⇒ y = 0

Geometrically