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If ω is the complex cube root of unity, find the value of (1 + ω)(1 + ω2)(1 + ω4)(1 + ω8)

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Best answer

ω is the complex cube root of unity.

ω3 = 1 and 1 + ω + ω2 = 0

Also, 1 + ω2 = -ω, 1 + ω = -ω2 and ω + ω2 = -1

(1 + ω)(1 + ω2)(1 + ω4)(1 + ω8)

= (1 + ω)(1 + ω2)(1 + ω)(1 + ω2) …..[∵ ω3 = 1, ω4 = ω]

= (-ω2)(-ω)(-ω2)(-ω)

= ω6 = (ω3)2

= (1)2

= 1

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