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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 argument of the complex number \[\frac{13-5i}{4-9i}\]is [MP PET 1997]

    A) \[\frac{\pi }{3}\]

    B)   \[\frac{\pi }{4}\]

    C) \[\frac{\pi }{5}\]

    D) \[\frac{\pi }{6}\]

    Correct Answer: B

    Solution :

    \[arg\left( \frac{13-5i}{4-9i} \right)=arg(13-5i)-arg(4-9i)\] \[=-{{\tan }^{-1}}\left( \frac{5}{13} \right)+{{\tan }^{-1}}\frac{9}{4}=\frac{\pi }{4}\]


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