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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
    The value of \[(1-\omega +{{\omega }^{2}})\,{{(1-{{\omega }^{2}}+\omega )}^{6}}\], where \[\omega ,{{\omega }^{2}}\] are cube roots of unity [DCE 2001]

    A) 128\[\omega \]

    B) \[-128{{\omega }^{2}}\]

    C) \[-128\omega \]

    D) \[128{{\omega }^{2}}\]

    Correct Answer: C

    Solution :

    \[(1-\omega +{{\omega }^{2}})\,{{(1-{{\omega }^{2}}+\omega )}^{6}}\]\[=(-2\omega )\,{{(-2{{\omega }^{2}})}^{6}}=-128\omega .\]


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