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Let ω be a non-real cube root of unity. Evaluate the expression (1 + 2ω + 3ω^2)/(2 + 3ω + 3ω^2) + (2 + 3ω + 3ω^2)/(3 + 3ω + 2ω^2).

1. −2ω
2. 2ω
3. ω
4. 0

Correct answer: −2ω

Solution

The expression simplifies using the properties of cube roots of unity, where ω satisfies ω^3 = 1 and 1 + ω + ω^2 = 0. By substituting and simplifying, the terms combine to yield -2ω, confirming that the correct option is indeed -2ω.

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