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

  • question_answer
    A point z moves on Argand diagram in such a way that |z -3i| \[=2,\] then its locus will be   [RPET 1992; MP PET 2002]

    A) \[y-\]axis

    B) A straight line

    C) A circle

    D) None of these

    Correct Answer: C

    Solution :

    \[|z-3i|=2,\]let \[z=x+iy\] Þ \[|x+i(y-3)|=2\] Squaring both sides, we get \[[{{x}^{2}}+{{(y-3)}^{2}}]=4\] Þ\[{{x}^{2}}+{{y}^{2}}-6y+5=0\]


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