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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Geometry of complex numbers

  • question_answer
    If \[w=\frac{z}{z-\frac{1}{3}i}\] and \[|w|=1\], then z lies on [AIEEE 2005]

    A) A straight line

    B) A parabola

    C) An ellipse

    D) A circle

    Correct Answer: A

    Solution :

    \[\left| \,\frac{z}{z-\frac{i}{3}}\, \right|=1\Rightarrow |z|=\left| \,z-\frac{i}{3}\, \right|\] Clearly locus of z is perpendicular bisector of line joining points having complex number \[0+i0\] and \[0+\frac{i}{3}\]. Hence z lies on a straight line.


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