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

  • question_answer
    The conjugate of complex number \[\frac{2-3i}{4-i},\] is [MP PET 2003]

    A) \[\frac{3i}{4}\]

    B) \[\frac{11+10i}{17}\]

    C) \[\frac{11-10i}{17}\]

    D) \[\frac{2+3i}{4i}\]

    Correct Answer: B

    Solution :

    \[\frac{2-3i}{4-i}=\frac{(2-3i)\,(4+i)}{(4+i)\,(4-i)}\]\[=\frac{8+3-12i+2i}{16+1}\]\[=\,\frac{11-10i}{17}\] Þ  Conjugate \[=\frac{11+10i}{17}\].


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