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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 cube roots of unity then \[{{\omega }^{2}}{{(1+\omega )}^{3}}-(1+{{\omega }^{2}})\omega =\] [Orissa JEE 2005]

    A) 1

    B) -1

    C) i

    D) 0

    Correct Answer: D

    Solution :

    \[{{\omega }^{2}}{{(1+\omega )}^{3}}-(1+{{\omega }^{2}})\omega ={{\omega }^{2}}{{(-{{\omega }^{2}})}^{3}}-\omega (-\omega )\] = \[-{{\omega }^{2}}+{{\omega }^{2}}=0\].


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