A) \[\frac{1}{2}+\frac{\sqrt{3}}{2}i\]
B) \[\frac{1}{2}-\frac{\sqrt{3}}{2}i\]
C) \[-\frac{1}{2}+\frac{\sqrt{3}}{2}i\]
D) None of these
Correct Answer: C
Solution :
Here \[-\frac{1}{2}+\frac{1}{2}i\sqrt{3}\] is one of the two imaginary cube root of unity. If we denote it by\[\omega \]. Then\[{{\omega }^{1000}}={{\omega }^{999}}\omega ={{({{\omega }^{3}})}^{333}}\omega =\omega =-\frac{1}{2}+\frac{\sqrt{3}}{2}i\].
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