{left( -frac{1}{2} + frac{sqrt{3}}{2}i right) | vedclass

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Question

(C) Let $\omega = -\frac{1}{2} + \frac{\sqrt{3}}{2}i$,which is a complex cube root of unity.We know that $\omega^3 = 1$.Now,${\left( -\frac{1}{2} + \f

Vedclass · Accepted Answer

$-\frac{1}{2} + \frac{\sqrt{3}}{2}i$

Vedclass · Answer

(C) Let $\omega = -\frac{1}{2} + \frac{\sqrt{3}}{2}i$,which is a complex cube root of unity.We know that $\omega^3 = 1$.Now,${\left( -\frac{1}{2} + \frac{\sqrt{3}}{2}i ight)^{1000}} = \omega^{1000}$.Since $1000 = 3 	imes 333 + 1$,we have $\omega^{1000} = (\omega^3)^{333} 	imes \omega^1$.$= (1)^{333} 	imes \omega = \omega$.Therefore,the result is $-\frac{1}{2} + \frac{\sqrt{3}}{2}i$.

${\left( -\frac{1}{2} + \frac{\sqrt{3}}{2}i \right)^{1000}} = .....$

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