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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 \[z=\frac{-2}{1+\sqrt{3}\,i}\] then the value of \[arg\,(z)\] is [ Orissa JEE 2002]

    A) \[\pi \]

    B) \[\pi /3\]

    C) \[2\pi /3\]

    D) \[\pi /4\]

    Correct Answer: C

    Solution :

    \[z=\frac{-2}{1+\sqrt{3}i}\]=\[\frac{-2}{1+\sqrt{3}i}\times \frac{1-\sqrt{3}i}{1-\sqrt{3}i}\]\[=\frac{-2+2\sqrt{3}i}{1+3}\] \[\Rightarrow z=\frac{-1}{2}+\frac{\sqrt{3}}{2}i\]\[\Rightarrow \,arg\,(z)={{\tan }^{-1}}\left( -\frac{\sqrt{3}/2}{1/2} \right)=\frac{2\pi }{3}\].


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