A) 1
B) w
C) \[{{w}^{2}}\]
D) None of these
Correct Answer: B
Solution :
[b] \[\because z={{\left( \frac{-1}{2}+\frac{\sqrt{3}i}{2} \right)}^{1000}}\] \[={{\left( \frac{-1+\sqrt{3}i}{2} \right)}^{1000}}\] \[\because \omega =\frac{-1+\sqrt{3}i}{2}\] \[z={{\left( \omega \right)}^{10000}}\] \[={{\omega }^{3\times 333+1}}\] \[=1.\omega =\omega \] Hence, option [b]is correct
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