A) an ellipse
B) a circle
C) a straight line
D) a parabola
Correct Answer: C
Solution :
As given \[\omega =\frac{z}{z-\frac{1}{3}i}\Rightarrow |\omega |=\frac{|z|}{|z-\frac{1}{3}i|}=1\] \[\Rightarrow \,\,\,|z|=\left| z-\frac{1}{3}i \right|\] \[\Rightarrow \] distance of z from origin and point \[\left( 0,\frac{1}{3} \right)\] is same hence z lies on bisector of the line joining points \[(0,0)\] and \[(0,1/3)\]. Hence, z lies on a straight line.You need to login to perform this action.
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