JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank De Moivre's theorem and Roots of unity

  • question_answer
    The roots of the equation \[{{x}^{4}}-1=0\],  are [MP PET 1986]

    A) \[1,\,1,i,-i\]

    B) \[1,\,-1,i,-i\]

    C) \[1,-1,\omega ,{{\omega }^{2}}\]

    D) None of these

    Correct Answer: B

    Solution :

    Given equation  \[{{x}^{4}}-1=0\] Þ \[({{x}^{2}}-1)({{x}^{2}}+1)=0\] Þ \[{{x}^{2}}=1\]and \[{{x}^{2}}=-1\] Þ \[x=\pm 1,\pm i\]


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