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If w is a non-real cube root of unity, find the value of (1 + w - w²)².

1. 4w
2. w
3. w²
4. -4w

Correct answer: 4w

Solution

Since 1 + w = -w², the bracket becomes 1 + w - w² = -w² - w² = -2w², and squaring gives 4w⁴ = 4w because w³ = 1.

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