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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  \[z\]  is a complex number, then \[(\overline{{{z}^{-1}}})(\overline{z})=\]

    A) 1

    B) -1

    C) 0

    D) None of these

    Correct Answer: A

    Solution :

    Let\[z=x+iy,\overline{z}=x-iy\]and \[{{z}^{-1}}=\frac{1}{x+iy}\] Þ \[(\overline{{{z}^{-1}}})=\frac{x+iy}{{{x}^{2}}+{{y}^{2}}}\];  \[\therefore \]\[(\overline{{{z}^{-1}}})\,\bar{z}=\frac{x+iy}{{{x}^{2}}+{{y}^{2}}}(x-iy)=1\]


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