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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 cube root of 1 is \[\omega \], then the value of \[{{(3+\omega +3{{\omega }^{2}})}^{4}}\] is [MP PET 2001]

    A) 0

    B) 16

    C) \[16\,\omega \]

    D) \[16\,{{\omega }^{2}}\]

    Correct Answer: C

    Solution :

    \[{{(3+\omega +3{{\omega }^{2}})}^{4}}\]\[=\,{{(-3\omega +\omega )}^{4}}\] \[[\because \,\,\omega +{{\omega }^{2}}=-1]\]                        = \[{{(-2\omega )}^{4}}=16{{\omega }^{4}}=16\omega \].


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