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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 [RPET 2001]

    A) 0

    B) \[\pi /6\]

    C) \[\pi /3\]

    D) \[\pi /2\]

    Correct Answer: D

    Solution :

    \[z=\frac{1+\sqrt{3}i}{\sqrt{3}-i}\]\[=\,\frac{1+\sqrt{3}i}{\sqrt{3}-i}\times \]\[\frac{\sqrt{3}+i}{\sqrt{3}+i}\]    \[=\frac{\sqrt{3}+i+3i-\sqrt{3}}{3+1}\]=\[\frac{4i}{4}=i\] amp\[(z)=\,\pi /2\]     \[[\because \,\tan \theta =b/a]\]


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