A) 0
B) \[-1\]
C) 2
D) \[-2\]
Correct Answer: D
Solution :
\[{{\left( \frac{\sqrt{3}+i}{2} \right)}^{6}}+{{\left( \frac{i-\sqrt{3}}{2} \right)}^{6}}\] \[={{\left( \frac{i\sqrt{3}+{{i}^{2}}}{2i} \right)}^{6}}+{{\left( \frac{{{i}^{2}}-i\sqrt{3}}{2i} \right)}^{6}}\] \[=\frac{1}{{{(i)}^{6}}}{{\left( \frac{-1+i\sqrt{3}}{2} \right)}^{6}}+\frac{1}{{{(i)}^{6}}}{{\left( \frac{-1-i\sqrt{3}}{2} \right)}^{6}}\] \[=-{{(\omega )}^{6}}-{{({{\omega }^{2}})}^{6}}\] \[=-{{\omega }^{6}}-{{\omega }^{12}}\] \[=-{{({{\omega }^{3}})}^{2}}-{{({{\omega }^{3}})}^{4}}\] \[=-1-1=-2\]
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