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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    The value of\[(2-\omega )(2-{{\omega }^{2}})(2-{{\omega }^{10}})(2-{{\omega }^{11}})\]where\[\omega \]is the complex cube root of unity, is:

    A)  49                                         

    B)  50

    C)  48                         

    D)         47

    E)  64   

    Correct Answer: A

    Solution :

    \[(2-\omega )(2-{{\omega }^{2}})(2-\omega )(2-{{\omega }^{2}})\] \[=(2-{{\omega }^{2}}){{(2-{{\omega }^{2}})}^{2}}\] \[={{\{(2-\omega )(2-{{\omega }^{2}})\}}^{2}}\] \[={{\{4-2(\omega +{{\omega }^{2}})+1\}}^{2}}\] \[={{\{4+2+1\}}^{2}}={{7}^{2}}\] \[=49\]


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