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Let z_r = cos(2*pi*r/5) + i*sin(2*pi*r/5) for r = 0, 1, 2, 3, 4 (the five fifth roots of unity). Find the product z₀*z₁*z₂*z₃*z₄.

1. -1
2. 0
3. 1
4. none of these

Correct answer: 1

Solution

Multiplying the five fifth roots of unity adds their arguments to 4*pi, a full multiple of 2*pi, giving a product of 1 (consistent with product of all n-th roots = (-1)^(n+1) = 1 for n = 5).

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