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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Conjugate, Modulus and Argument of complex number

  • question_answer
    If the conjugate of \[(x+iy)(1-2i)\]be \[1+i\], then [MP PET 1996]

    A) \[x=\frac{1}{5}\]

    B)   \[y=\frac{3}{5}\]

    C) \[x+iy=\frac{1-i}{1-2i}\]

    D)   \[x-iy=\frac{1-i}{1+2i}\]

    Correct Answer: C

    Solution :

    Given that \[\overline{(x+iy)(1-2i)}=1+i\] Þ  \[x-iy=\frac{1+i}{1+2i}\Rightarrow x+iy=\frac{1-i}{1-2i}\].


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