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The complex numbers z=x+iy which satisfy...

The complex numbers `z=x+iy` which satisfy the equation `|(z-5i)/(z+5i)|=1` lie on

A

the axis of x

B

the straight line x=5

C

the circle passing through the origin.

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have

`|(z-5i)/(z+5i)|=1`
`rArr |z-5i|=|z+5i|`
`rArr` PA=PB
`rArr` P lies on the perpendicular bisector AB, which is x-axis.
Hence, `|(z-5i)/(x+5i)|=1` represents x-axis.
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