If \( \omega \) is the complex cube root of unity, then the value of \[ \omega+\omega^{\left(\fr...

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If \( \omega \) is the complex cube root of unity, then the value of
\[
\omega+\omega^{\left(\frac{1}{2}+\frac{3}{8}+\frac{9}{32}+\frac{27}{128}+\ldots .\right)}
\]
(A) \( -1 \)
(B) 1
(C) \( -i \)
(D) \( i \)
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