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$(1 - ω + ω^{2}) (1 - ω^{2} + ω^{4}) (1 - ω^{4} + ω^{8}) . . . . to 2 n factors =$

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$2^{2 n}$

$2^{n}$

answer is B.

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Detailed Solution

$(1 - w + w^{2}) (1 - w^{2} + w^{4}) (1 - w^{4} + w^{8}) . . . . 2 n$ facton.

$\begin{array}{rcl} (1 + w^{2} - w) (1 + w^{4} - w^{2}) . . . . \\ (- w - w) (- w^{2} - w^{2}) . . . . . \\ = & (- 2 w) (- 2 w^{2}) . . . . \\ = & 2^{2} \cdot 2^{2} . . . . n times \\ = & 2^{2 n} \end{array}$

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