If 1, ω, ω² are the cube roots of unity, then the value of (1 + ω) (1 + ω²) (1 + ω⁴) (1 + ω⁸) is

Question

Question

Answer 1

Concept:

If 1, ω, ω² are the cube roots of unity

Calculation:

We have to find the value of (1 + ω) (1 + ω²) (1 + ω⁴) (1 + ω⁸)

⇒ (1 + ω) (1 + ω²) (1 + ω⁴) (1 + ω⁸)

= [(1 + ω) (1 + ω²)] × [(1 + ω³ × ω) (1 + (ω³)² ω²)]

= [(1 + ω) (1 + ω²)] × [(1 + ω) (1 + ω²)] (∵ω³ = 1)

= (1 + ω + ω² + ω³) × (1 + ω + ω² + ω³)

= (0 + 1) × (0 + 1)

= 1 × 1 = 1