A) \[20\sqrt{3}i\]
B) 1
C) \[\frac{1}{{{2}^{19}}}\]
D) \[-1\]
Correct Answer: D
Solution :
As \[\frac{-1+i\sqrt{3}}{2}=\omega \]and \[\frac{-1-i\sqrt{3}}{2}={{\omega }^{2}}\] \[\therefore \,\,\,{{(\omega )}^{20}}+{{({{\omega }^{2}})}^{20}}={{\omega }^{18}}.{{\omega }^{2}}+{{\omega }^{39}}.\omega ={{\omega }^{2}}+\omega =-1\]
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