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,\[{{(1+\omega -{{\omega }^{2}})}^{7}}={{(-{{\omega }^{2}}-{{\omega }^{2}})}^{7}}\] \[={{(-2)}^{7}}{{({{\omega }^{2}})}^{7}}\] \[=-128\,\,{{\omega }^{2}}\]You need to login to perform this action.
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