Question

if w is a complex no cube root of unity show that (2-w) (2-w^2) = 7​

Answer 1

Answer:

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if w is a complex cube root of unity show that (2-w) (2-w^2)=7

Answers : (1)

Since w is a non-real complex root of unity, then w ≠ 1, so

w² + w + 1 = 0

So when w is a non-real complex root of unity, we have:

w³ = 1

w² + w + 1 = 0

(2−w)(2−w²)

= w³ − 2w² − 2w + 4

= w³ − 2w² − 2w − 2 + 6

= w³ − 2(w² + w + 1) + 6

= 1 − 2(0) + 6

= 7

Step-by-step explanation:

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