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प्रश्न
If ω ≠ 1 is a cube root of unity, show that (1 + ω)(1 + ω2)(1 + ω4)(1 + ω8)….. (1 + ω2n) = 1
उत्तर
(1 + ω)(1 + ω2)(1 + ω4)(1 + ω8) …… (1 + ω2n)
= (1 + ω)(1 + ω2)(1 + ω4)(1 + ω8) ……. 2n factors
= (– ω2)(– ω)(– ω2)(– ω) …… 2n factors
= ω3. ω3
= 1
Hence proved.
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