Question

Where does z lie, if |(z - 5i)/(z + 5i)| = 1.

Answer 1

Given |(z - 5i)/(z + 5i)| = 1.

⇒ |z – 5i| = |z + 5i|

⇒ |x + iy – 5i| = |x + iy + 5i|

⇒ |x + i (y – 5) |² = |x + i (y + 5) |²

⇒ x² + (y – 5)² = x² + (y + 5)²

⇒ 20y = 0

⇒ y = 0

∴ z lies on the x – axis.