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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 values of \[x\] and \[y\] for which the numbers \[3+i{{x}^{2}}y\] and \[{{x}^{2}}+y+4i\] are conjugate complex can be

    A) \[(-2,-1)\]or \[(2,-1)\]

    B) \[(-1,\text{ }2)\]or \[(-2,\text{ }1)\]

    C) \[(1,\,2)\]or \[(-1,-2)\]

    D) None of these

    Correct Answer: A

    Solution :

    According to condition,  \[3-i{{x}^{2}}y={{x}^{2}}+y+4i\] Þ \[{{x}^{2}}+y=3\]and \[{{x}^{2}}y=-4\] Þ \[x=\pm 2,y=-1\] Þ \[(x,y)=(2,-1)\]or \[(-2,-1)\]


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