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Let alpha be a primitive (non-real) fifth root of unity and let beta be a primitive (non-real) fourth root of unity. Evaluate (1 + alpha)(1 + beta)(1 + alpha²)(1 + beta²)(1 + beta³)(1 + alpha⁴).

1. 0
2. (1 + alpha + alpha²)(1 - beta²)
3. (1 + alpha)(1 + beta + beta²)
4. 1

Correct answer: 0

Solution

Since beta is a primitive 4th root of unity, beta² = -1, so the factor (1 + beta²) = 0 makes the entire product 0.

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