A) A circle of radius 1
B) An ellipse with foci at \[(1,\,0)\] and (0, - 1)
C) A straight line through the origin
D) A circle on the line joining \[(1,\,0),(0,\,1)\] as diameter
Correct Answer: C
Solution :
\[|z-1|\,=\,|z+i|\] Þ \[|x-1+iy{{|}^{2}}=\,|x+i(y+1){{|}^{2}}\] Þ \[{{(x-1)}^{2}}+{{y}^{2}}={{x}^{2}}+{{(y+1)}^{2}}\] Þ \[x+y=0\] i.e., a straight line through the origin.
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