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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 the cube root of unity, then \[{{(3+5\omega +3{{\omega }^{2}})}^{2}}\] + \[{{(3+3\omega +5{{\omega }^{2}})}^{2}}\] = [MP PET 1999]

    A) 4

    B) 0

    C) - 4

    D) None of these

    Correct Answer: C

    Solution :

    \[{{(3+5\omega +3{{\omega }^{2}})}^{2}}+{{(3+3\omega +5{{\omega }^{2}})}^{2}}\] \[={{(3+3\omega +3{{\omega }^{2}}+2\omega )}^{2}}+{{(3+3\omega +3{{\omega }^{2}}+2{{\omega }^{2}})}^{2}}\] \[(1+\omega +{{\omega }^{2}}=0,{{\omega }^{3}}=1)\] \[={{(2\omega )}^{2}}+{{(2{{\omega }^{2}})}^{2}}=4{{\omega }^{2}}+4{{\omega }^{4}}=4(-1)=-4\].


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