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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 amplitude of \[\frac{1+\sqrt{3}\,i}{\sqrt{3}+i}\] is [DCE 1999; Karnataka CET 2005]

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

    B) \[-\frac{\pi }{6}\]

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

    D) None of these

    Correct Answer: A

    Solution :

    \[amp\,\left( \frac{1+\sqrt{3}\,i}{\sqrt{3}+i} \right)\]\[=amp(1+\sqrt{3}\,i\,)-amp(\sqrt{3}+i)\] \[=\frac{\pi }{3}-\frac{\pi }{6}=\frac{\pi }{6}\].


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