KVPY Sample Paper KVPY Stream-SX Model Paper-19

  • question_answer
    If \[\operatorname{Re}\left( \frac{z-2i}{z+1} \right)=1,\] then the locus of the point representing z in the complex plane is -

    A) Circle

    B) a straight line

    C) Parabola

    D) none of these

    Correct Answer: B

    Solution :

    \[\operatorname{Re}\left( \frac{z-2i+1-1}{z+1} \right)=1\]\[\Rightarrow \operatorname{Re}\left( \frac{-1-2i}{z+1}+1 \right)=1\]\[\Rightarrow \operatorname{Re}\left( \frac{-1-2i}{z+1} \right)=0\]\[\Rightarrow x+1+2y=0\]

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