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  4. lf w=(z/z-(i)3) and |w|=1, then z lies on

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Q. lf $ w=\frac{z}{z-\frac{i}{3}} $ and $ |w|=1, $ then z lies on

Rajasthan PETRajasthan PET 2007

Solution:

Given, $ w=\frac{z}{z-\frac{i}{3}} $ and $ |w|=1 $
$ \left| \frac{z}{z-\frac{i}{3}} \right|=1\Rightarrow |z|=\left| z-\frac{i}{3} \right| $
z lies on the perpendicular bisector of the line joining the points (0, 0) and (0, 1/3). So, z lies on a line.