A) \[-1\]
B) 1
C) 0
D) 2
E) none of these
Correct Answer: A
Solution :
\[{{\left( \frac{-1+\sqrt{-3}}{2} \right)}^{26}}+{{\left( \frac{-1-\sqrt{-3}}{2} \right)}^{26}}\] \[={{\left( \frac{-1+\sqrt{3}i}{2} \right)}^{26}}+{{\left( \frac{-1-\sqrt{3}i}{2} \right)}^{26}}\] \[={{\omega }^{26}}+{{({{\omega }^{2}})}^{26}}\] \[={{\omega }^{3\times 8+2}}+{{\omega }^{3\times 17+1}}\] \[={{\omega }^{2}}+\omega =-1\] \[(\because 1+\omega +{{\omega }^{2}}=0)\]
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