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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 \[\omega \] is an imaginary cube root of unity, \[{{(1+\omega -{{\omega }^{2}})}^{7}}\]equals [IIT 1998; MP PET 2000]

    A) \[128\omega \]

    B) \[-128\omega \]

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

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

    Correct Answer: D

    Solution :

    \[{{(1+\omega -{{w}^{2}})}^{7}}={{(1+\omega +{{\omega }^{2}}-2{{\omega }^{2}})}^{7}}={{(-2{{\omega }^{2}})}^{7}}\] \[=-128{{\omega }^{14}}=-128{{\omega }^{12}}{{\omega }^{2}}=-128{{\omega }^{2}}\]


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