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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2007

  • question_answer
    lf\[w=\frac{z}{z-\frac{i}{3}}\]and\[|w|=1,\] then z lies on

    A)  a ellipse           

    B)  a circle

    C)  a straight line     

    D)  a parabola

    Correct Answer: C

    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.


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