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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  \[1,\omega ,{{\omega }^{2}}\] are the three cube roots of unity, then \[{{(3+{{\omega }^{2}}+{{\omega }^{4}})}^{6}}=\] [MP PET 1995]

    A) 64

    B) 729

    C) 2

    D) 0

    Correct Answer: A

    Solution :

    \[{{(3+{{\omega }^{2}}+{{\omega }^{4}})}^{6}}={{(3+{{\omega }^{2}}+\omega )}^{6}}={{(3-1)}^{6}}=64\]


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