If w is a complex root of z^5 = 1 with w != 1, evaluate 1 + w + w^2 + w^3 + w^4.
Answer and explanation
Correct answer: D. 0
- Step 1: Sum of a geometric progression: S = (w^5 - 1) / (w - 1). Step 2. Since w is a root of z^5 = 1, w^5 = 1. As w != 1, w - 1 != 0, so S = (1 - 1) / (w - 1) = 0. Answer: 0. Why not the others: The sum of all nth roots of unity is always identically zero.
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