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

  • question_answer
    If w is a complex cube root of unity, then \[(1-\omega )(1-{{\omega }^{2}})\] \[(1-{{\omega }^{4}})(1-{{\omega }^{8}})=\]

    A) 0

    B) 1

    C) - 1

    D) 9

    Correct Answer: D

    Solution :

    \[(1-\omega )(1-{{\omega }^{2}})(1-{{\omega }^{4}})(1-{{\omega }^{8}})\] \[=(1-\omega )(1-{{\omega }^{2}})(1-\omega )(1-{{\omega }^{2}})={{(1-\omega )}^{2}}{{(1-{{\omega }^{2}})}^{2}}\] = \[(-3\omega )(-3{{\omega }^{2}})=9{{\omega }^{3}}=9\].


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