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With i = sqrt(-1) and w = -1/2 + i*sqrt(3)/2 (a primitive cube root of unity), evaluate 4 + 5*w³³⁴ + 3*w³⁶⁵.

1. 1 - i*sqrt(3)
2. -1 + i*sqrt(3)
3. i*sqrt(3)
4. -i*sqrt(3)

Correct answer: 1 - i*sqrt(3)

Solution

Reducing exponents gives 4 + 5w + 3w²; using w² = -1 - w and the value of w yields 1 - i*sqrt(3).

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