A) a circle of radius 1
B) an ellipse with foci at 1 and \[-i\]
C) a line through the origin
D) a circle on the line joining 1 and \[-i\] as diameter
Correct Answer: C
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.
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