A) 0
B) 1
C) 2
D) 3
E) \[-2\]
Correct Answer: C
Solution :
We know\[-\frac{1}{2}+i\frac{\sqrt{3}}{2}=\omega \]and\[-\frac{1}{2}-i\frac{\sqrt{3}}{2}={{\omega }^{2}}\] \[\therefore \] \[{{\left[ \frac{-1+i\sqrt{3}}{2} \right]}^{3n}}+{{\left[ \frac{1-i\sqrt{3}}{2} \right]}^{3n}}\] \[={{\omega }^{3n}}+{{({{\omega }^{2}})}^{3n}}\] \[={{({{\omega }^{3}})}^{n}}+{{[{{({{\omega }^{3}})}^{n}}]}^{2}}\] \[=1+1=2\]You need to login to perform this action.
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