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"PSN network out? Is It Still Down? Find Out Now Before Millions Are Left in the Dark! - Aurero

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 Thus, the vector is $ \boxed{\left\langle \dfrac{4}{7}, \dfrac{1}{7}, -\dfrac{2}{7} \right\rangle} $.

📌 Question: Among all roots of the polynomial $ z^6 - z^4 + z^2 - 1 = 0 $, a historian of mathematical astronomy seeks the maximum imaginary part, expressed as $ \sin \theta $ for $ 0 < \theta < \pi $. Find $ \theta $.

📌 Solution: Consider the polynomial:

📌 z^6 - z^4 + z^2 - 1 = 0

📌 So the roots satisfy either $ z^2 - 1 = 0 $ or $ z^4 + 1 = 0 $.

📌 Roots from $ z^2 - 1 = 0 $:

📌 $ z = \pm 1 $, both real, so imaginary part is 0.

📌 Roots from $ z^4 = -1 $:

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