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Question

The locus represented by |z-1|=|z+i| is

A
a circle of radius 1
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B
an ellipse with foci at (1, 0) and (0, –1)
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C
a straight line through the origin
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D
a circle on the line joining (1, 0), (0, 1) as diameter
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Solution

The correct option is C a straight line through the origin
|z-1|=|z-i|
locus of z is perpendicular bisector.

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