If ω is the complex cube root of unity, find the value of (1 + ω)(1 + ω^2)(1 + ω^4)(1 + ω^8)
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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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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