1.

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

Answer»

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.



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