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Home » Substituer \( x = 4 \) dans \( y = 10 - 2x \) : - Abu Waleed Tea

Substituer \( x = 4 \) dans \( y = 10 - 2x \) : - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 5Question: An AI-powered medical imaging system processes a signal modeled by the complex number $ z = \cos\left(\frac{\pi}{6}\right) + i \sin\left(\frac{\pi}{6}\right) $. Compute $ z^6 $ and express it in the form $ a + bi $.

📌 Solution: Using De Moivre's Theorem, $ z^n = \cos\left(n\theta\right) + i \sin\left(n\theta\right) $. Here, $ z = \cos\left(\frac{\pi}{6}\right) + i \sin\left(\frac{\pi}{6}\right) $, so $ z^6 = \cos\left(6 \cdot \frac{\pi}{6}\right) + i \sin\left(6 \cdot \frac{\pi}{6}\right) = \cos(\pi) + i \sin(\pi) $. Evaluating, $ \cos(\pi) = -1 $ and $ \sin(\pi) = 0 $, so $ z^6 = -1 + 0i $.

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