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

  • question_answer
    The locus of \[z\] given by \[\left| \frac{z-1}{z-i} \right|=1\],  is [Roorkee 1990]

    A) A circle

    B) An ellipse

    C) A straight line

    D) A parabola

    Correct Answer: C

    Solution :

    \[\left| \frac{z-1}{z-i} \right|=1\]Þ \[|z-1|\,=\,|z-i|\] Þ\[|(x-1)+iy|\,=\,|x+i(y-1)|\] Þ \[\sqrt{{{(x-1)}^{2}}+{{y}^{2}}}=\sqrt{{{x}^{2}}+{{(y-1)}^{2}}}\] Þ \[2x=2y\]or \[x-y=0\] Which is the equation of a straight line.


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