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Question

If z=x+iy is a complex number which satisfy |z5i||z+5i|=1, then z lies on 


A
the real axis
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B
the straight line, y=5
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C
a circle passing through the origin
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D
the imaginary axis
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Solution

The correct option is D the real axis
Given : |z5i||z+5i|=1
|z5i|=|z+5i|
So, z is the perpendicular bisector of line segment joning (0,5) and (0,5)
Therefore, the locus of z is 
y=0
Which is x axis.

Mathematics

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