If ω is the complex cube root of unity, show that (2 – ω)(2 – ω^2) = 7
If ω is the complex cube root of unity, show that (2 – ω)(2 – ω2) = 7
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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
L.H.S. = (2 – ω)(2 – ω2)
= 4 – 2ω2 – 2ω + ω3
= 4 – 2(ω2 + ω) + 1
= 4 – 2(-1) + 1
= 4 + 2 + 1
= 7
= R.H.S.
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