A) \[-{{2}^{2010}}\]
B) \[{{2}^{2010}}\]
C) \[1\]
D) \[-1\]
Correct Answer: B
Solution :
\[x+iy={{(-1+i\sqrt{3})}^{2010}}\] \[\Rightarrow \] \[x+iy={{(2)}^{2010}}{{\left( \frac{-1+i\sqrt{3}}{2} \right)}^{2010}}\] \[\left( \because \,\,\,\omega =\frac{-1+i\sqrt{3}}{2} \right)\] \[\Rightarrow \] \[(x+iy)={{(2)}^{2010}}{{\omega }^{2010}}\] \[\Rightarrow \] \[(x+iy)={{(2)}^{2010}}{{({{\omega }^{3}})}^{670}}\] \[(\because \,\,{{\omega }^{3}}=1)\] \[\Rightarrow \] \[(x+iy)={{(2)}^{2010}}{{(1)}^{670}}={{2}^{2010}}+i.0\] On comparing real part \[\Rightarrow \] \[x={{2}^{2010}}\]
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