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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • 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 :

                    We have \[{{(1+\omega -{{\omega }^{2}})}^{7}}={{(-{{\omega }^{2}}-{{\omega }^{2}})}^{7}}\] \[={{(-2)}^{7}}{{({{\omega }^{2}})}^{7}}\] \[=128{{\omega }^{2}}\]              


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