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JCECE Engineering JCECE Engineering Solved Paper-2006

  • question_answer
    If \[\omega \] is an imaginary cube root of unity, then \[{{(1+\omega -{{\omega }^{2}})}^{7}}\]equals:

    A) \[128\omega \]                

    B) \[-128\omega \]

    C) \[128{{\omega }^{2}}\]                 

    D) \[-128{{\omega }^{2}}\]

    Correct Answer: D

    Solution :

    Key Idea: The cubic roots of unity are\[1,\,\,\omega ,\,\,{{\omega }^{2}}\]and\[1+\omega +{{\omega }^{2}}=0\]. We have,\[{{(1+\omega -{{\omega }^{2}})}^{7}}={{(-{{\omega }^{2}}-{{\omega }^{2}})}^{7}}\]                                            \[={{(-2)}^{7}}{{({{\omega }^{2}})}^{7}}\]                                            \[=-128\,\,{{\omega }^{2}}\]


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