A) 32
B) -64
C) 64
D) 0
Correct Answer: D
Solution :
Given that \[2x=-1+\sqrt{3}i\] \[\Rightarrow \] \[x=\frac{-1+\sqrt{3}i}{2}\] \[=\omega \] \[\therefore \] \[{{(1-{{x}^{2}}+x)}^{6}}-{{(1-x+{{x}^{2}})}^{6}}\] \[={{(1-{{\omega }^{2}}+\omega )}^{6}}-{{(1-\omega +{{\omega }^{2}})}^{6}}\] \[={{(-2{{\omega }^{2}})}^{6}}-{{(-2\omega )}^{6}}\] ( \[\because \] \[1+\omega +{{\omega }^{2}}=0\]) \[={{2}^{6}}\,{{\omega }^{12}}-{{2}^{6}}{{\omega }^{6}}\] \[={{2}^{6}}(1)-{{2}^{6}}(1)\] (\[\because \] \[{{\omega }^{3}}=1\]) \[=0\]
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