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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 a cube root of unity, then \[(1+\omega -{{\omega }^{2}})\] \[(1-\omega +{{\omega }^{2}})\] =                 [MNR 1990; MP PET 1993, 2002]

    A) 1

    B) 0

    C) 2

    D) 4

    Correct Answer: D

    Solution :

    If \[\omega \] is a complex cube root of unity then \[{{\omega }^{3}}=1\] and \[1+\omega +{{\omega }^{2}}=0\], therefore \[(1+\omega -{{\omega }^{2}})(1-\omega +{{\omega }^{2}})\] \[=(-2{{\omega }^{2}})(-2\omega )=4\]


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