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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2004

  • question_answer
    If \[\omega =\frac{-1+\sqrt{3}i}{2}\] then \[{{(3+\omega +3{{\omega }^{2}})}^{4}}\] is :

    A)  16                                         

    B)  - 16

    C)  \[16\,\omega \]                              

    D)  \[16\,{{\omega }^{2}}\]

    Correct Answer: C

    Solution :

    Given that, \[\omega =\frac{-1+\sqrt{3}\,i}{2}\] \[\therefore \]  \[{{(3+\omega +3\,{{\omega }^{2}})}^{4}}\] \[={{\left[ 3+\left( \frac{-1+\sqrt{3}\,i}{2} \right)+{{\left( \frac{-1+\sqrt{3\,i}}{2} \right)}^{2}} \right]}^{4}}\] \[=16\,\omega \]


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