If \(a_1, a_2, ..., a_8\) are the roots of the equation \(x^8 + x^7 + ... + x + 1 = 0\), then the value of \(a_1^{2025} + a_2^{2025} + ... + a_8^{2025}\) is
Question and options
If are the roots of the equation , then the value of is
- 0
- 2
- 8
- 4
Answer and explanation
Correct answer: C - 8
The roots are the 9th roots of unity other than 1, so a_i^9 = 1. Since 2025 = 9*225, each a_i^2025 = 1, and the sum is 8.
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