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If $\omega$ is a complex cube root of unity, then $(1+\omega)\left(1+\omega^2\right) \quad\left(1+\omega^4\right)\left(1+\omega^8\right) \ldots$ to $2 n$ factors $=$
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$1$
$(1+\omega)\left(1+\omega^2\right)\left(1+\omega^4\right)\left(1+\omega^8\right) \ldots \ldots$ upto $2 n$ factors $=\left(-\omega^2\right)(-\omega)(1+\omega)\left(1+\omega^2\right) \ldots .$. upto $2 n$ factors
$=1.1 .1 . . .$. upto $n$ factors $=1$
$=1.1 .1 . . .$. upto $n$ factors $=1$
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