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

  • question_answer
    Let \[z\] be a purely imaginary number such that \[\operatorname{Im}(z)<0\]. Then  \[arg\,(z)\] is equal to

    A) \[\pi \]

    B) \[\frac{\pi }{2}\]

    C) 0

    D) \[-\frac{\pi }{2}\]

    Correct Answer: D

    Solution :

    Let\[z=0+ib\], where\[b<0\]. Then \[z\] is represented by a point on \[O{Y}'\] (negative direction of \[y-\]axis), therefore\[arg(z)=-\frac{\pi }{2}\].


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