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  4. The locus represented by the equation |z-1|=|z-i| is

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Q. The locus represented by the equation $ |z-1|=|z-i| $ is

J & K CETJ & K CET 2004

Solution:

Given, $ |z-1|=|z-i| $
$ \Rightarrow $ z lies on the perpendicular bisector of the line joining $ (1,0) $ and $ (0,1) $ and is a straight line passing through origin.