A) 3
B) 1
C) 0
D) None of these
Correct Answer: C
Solution :
Let \[n=3k+1\] \[{{\omega }^{n}}+{{\omega }^{2n}}={{\omega }^{3k+1}}+{{\omega }^{2(3k+1)}}={{\omega }^{3k}}\omega +{{\omega }^{6k}}{{\omega }^{2}}\] \[={{({{\omega }^{3}})}^{k}}.\omega +{{({{\omega }^{3}})}^{2k}}\].\[{{\omega }^{2}}=\omega +{{\omega }^{2}}=-1\] Hence \[1+{{\omega }^{n}}+{{\omega }^{2n}}=1-1=0\]You need to login to perform this action.
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