If - is an imaginary cube root of unity then find- 1-21-2-41-4-8 - to 2n factors -

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Properties of Modulus

If ω is an ...

Question

If $ω$ is an imaginary cube root of unity then find: $(1 - ω + ω^{2}) (1 - ω^{2} + ω^{4}) (1 - ω^{4} + ω^{8})$ ..... to 2n factors $=$

2^{n + 1}

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2^{2 n}

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2^{2 n + 1}

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2^{n}

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Solution

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Similar questions

1, ω, ω^{2}

(1 - ω + ω^{2}) (1 - ω^{2} + ω^{4}) (1 - ω^{4} + ω^{8}) . . .

2 n

=

1, ω, ω^{2}

(1 - ω + ω^{2}) (1 - ω^{2} + ω^{4}) (1 - ω^{4} + ω^{8}) \dots . . .

(1 - ω + ω^{2}) (1 - ω^{2} + ω^{4}) (1 - ω^{4} + ω^{8}) . . . . . .

1, ω, ω^{2}

(1 + ω) (1 + ω^{2}) (1 + ω^{4}) (1 + ω^{8}) . . .

2 n

=

ω

ω

ω^{2}

(1 + ω^{4}

(1 + ω^{8}

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