If $\omega$ is a complex root of the equation $\mathcal{z}^{3} = 1,\ then\ \omega + \omega^{\left( \frac{1}{2} + \frac{3}{8} + \frac{9}{32} + \frac{27}{128} + ... \right)}\$ is equal to

Question

Dr. Abubacker · Accepted Answer

(a)
$\omega + \omega^{\left( \frac{1}{2} + \frac{3}{8} + \frac{9}{32} + \frac{27}{128} + ... \right)\ }$
$= \omega + \omega^{\left( \frac{1/2}{1 - 3/4} \right)}$
$= \omega + \omega^{2} = - 1\ \ \ \ \ (\because 1 + \omega + \omega^{2} = 0)$

Q. If $\omega$ is a complex root of the equation $\mathcal{z}^{3} = 1,\ then\ \omega + \omega^{\left( \frac{1}{2} + \frac{3}{8} + \frac{9}{32} + \frac{27}{128} + ... \right)}\$ is equal to

Explanation

Reviewed by Dr. Abubacker

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