A) One solution
B) 3 solutions
C) 2 solutions
D) No solution
Correct Answer: A
Solution :
From \[|z-1|=|z-2|\] Þ \[|x+iy-1|=|x+iy-2|\] Þ \[{{(x-1)}^{2}}+{{y}^{2}}={{(x-2)}^{2}}+{{y}^{2}}\]Þ \[x=\frac{3}{2}\] Similarly from \[|z-1|=|z-i|\]; \[x=y\] Hence, \[x=\frac{3}{2},\,y=\frac{3}{2}\] Therefore only one solution for the equation.
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