Question

Why is 1+ω ≠ ω+1? Explain it or an extended number line.

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Answer 1

Answer:

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1 - ω + ω² = -2ω,    as  1+ω²+ω = 0,  1+ω² = -ω

1 + ω - ω² = -2ω²    as 1 + ω = -ω²

So (1 - ω + ω²) (1 + ω - ω²) = -2ω * -2ω² = 4 ω³ = 4

Answer 2

1 - ω + ω² = -2ω,    as  1+ω²+ω = 0,  1+ω² = -ω

1 + ω - ω² = -2ω²    as 1 + ω = -ω²

So (1 - ω + ω²) (1 + ω - ω²) = -2ω * -2ω² = 4 ω³ = 4