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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 complex cube root of unity, then\[225+\]\[{{(3\omega +8{{\omega }^{2}})}^{2}}\]\[+{{(3{{\omega }^{2}}+8\omega )}^{2}}=\] [EAMCET 2003]

    A) 72

    B) 192

    C) 200

    D) 248

    Correct Answer: D

    Solution :

    \[225+{{(3\omega +8{{\omega }^{2}})}^{2}}+{{(3{{\omega }^{2}}+8\omega )}^{2}}\] \[=225+{{(5{{\omega }^{2}}-3)}^{2}}+{{(5\omega -3)}^{2}}\] \[=225+18-5(\omega +{{\omega }^{2}})\] \[=225+18-5(-1)=225+18+5=248.\]


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