If \( 1, \omega \) and \( \omega^{2} \) are cube roots of unity, sh...

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If \( 1, \omega \) and \( \omega^{2} \) are cube roots of unity, show that
\[
(1+\omega)\left(1+\omega^{2}\right)\left(1+\omega^{4}\right)\left(1+\omega^{8}\right) \ldots \text { upto } 2 n \text { factors }=1
\]
\( \mathrm{P} \)
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