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

  • question_answer
    \[POQ\] is a straight line through the origin \[O,\,\,P\] and \[Q\] represent the complex numbers \[a+ib\] and\[c+id\] respectively and \[OP=OQ\],  then

    A) \[|a+ib|\,=\,|c+id|\]

    B) \[a+c=b+d\]

    C) \[arg(a+ib)=arg(c+id)\]

    D) None of these

    Correct Answer: B

    Solution :

     It is given that \[OP=OQ\] \[\therefore \,\,|\overrightarrow{OP}|\,=\,|\overrightarrow{OQ}|\]Þ \[|a+ib|\,=\,|c+id|\] Also \[\overrightarrow{OP}=-\overrightarrow{OQ},\,\,\,\,\therefore \overrightarrow{OP}+\overrightarrow{OQ}=0\] Þ \[(a+c)+i(b+d)=0\]Þ \[a+c=0=b+d\]


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