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

```
3 years ago

Arun
25768 Points
```							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
```
3 years ago
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• Test paper with Video Solution
• Mind Map
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