If ω is the complex cube root of unity, show that (2 – ω)(2 – ω

1.	If ω is the complex cube root of unity, show that (2 – ω)(2 – ω2) = 7
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 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.

If ω is the complex cube root of unity, show that (2 – ω)(2 – ω2) = 7

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

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.