Product Over Roots of Unity Polynomial

2175ExpertPolynomialsComplex Numbers

AIME II · 2023 · Problem 8

Let $\omega = \cos\frac{2\pi}{7} + i \cdot \sin\frac{2\pi}{7},$ where $i = \sqrt{-1}.$ Find the value of the product $$\prod_{k=0}^6 \left(\omega^{3k} + \omega^k + 1\right).$$

0 students attempted0% solvedRating 2175

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Product Over Roots of Unity Polynomial

2175ExpertPolynomialsComplex Numbers

AIME II · 2023 · Problem 8

Let $\omega = \cos\frac{2\pi}{7} + i \cdot \sin\frac{2\pi}{7},$ where $i = \sqrt{-1}.$ Find the value of the product $$\prod_{k=0}^6 \left(\omega^{3k} + \omega^k + 1\right).$$

0 students attempted0% solvedRating 2175