A) 3
B) 6
C) 9
D) 12
Correct Answer: C
Solution :
[c] \[\because (1-\omega )(1-{{\omega }^{2}})(1-{{\omega }^{4}})(1-{{\omega }^{5}})\] \[=(1-\omega )(1-{{\omega }^{2}})(1-{{\omega }^{3}}.\omega )(1-{{\omega }^{3}}.{{\omega }^{2}})\] \[=(1-{{\omega }^{2}}){{(1-{{\omega }^{2}})}^{2}}[\therefore 1-{{\omega }^{3}}=0]\] \[={{[(1-\omega )(1-{{\omega }^{2}})]}^{2}}\] \[={{(1-\omega -{{\omega }^{2}}+{{\omega }^{3}})}^{2}}1+\omega +{{\omega }^{2}}=0\] \[=\{1-(\omega -{{\omega }^{2}})+{{\omega }^{3}}\}\,\,\omega +{{\omega }^{2}}=-1\] \[={{\{1-(-1)+1\}}^{2}}={{3}^{2}}=9.\] Thus, the option [c] is correct.
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