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Home » Wait â ist die Implikation also **immer wahr**? - ToelettAPP

Wait â ist die Implikation also immer wahr? - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Let \(\omega\) be a root of \(x^2 - x + 1 = 0\). Then \(\omega^2 = \omega - 1\), and \(\omega^3 = \omega(\omega - 1) = \omega^2 - \omega = (\omega - 1) - \omega = -1\). So \(\omega^3 = -1\), and \(\omega^6 = 1\).

📌 Now evaluate at \(x = \omega\):

📌 \omega^4 + 3\omega^3 - 2\omega^2 + \omega + 5 = a\omega + b

📌 We compute each term:

📌 \(\omega^4 = \omega \cdot \omega^3 = \omega(-1) = -\omega\)

📌 \(3\omega^3 = 3(-1) = -3\)

📌 \(-2\omega^2 = -2(\omega - 1) = -2\omega + 2\)

📌 \(\omega\)

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