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

    A) 0

    B) \[\omega \]

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

    D) None of these

    Correct Answer: A

    Solution :

    \[{{(1+\omega )}^{3}}-{{(1+{{\omega }^{2}})}^{3}}={{(-{{\omega }^{2}})}^{3}}-{{(-\omega )}^{3}}\] \[=-{{\omega }^{6}}+{{\omega }^{3}}=-{{\omega }^{3}}{{\omega }^{3}}+{{\omega }^{3}}=-1+1=0\]


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