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Home » Shocked You’ve Been Missing This Top & Bralette GEM: Perfect Fit, Unmatched Style! - Tacotoon

Shocked You’ve Been Missing This Top & Bralette GEM: Perfect Fit, Unmatched Style! - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 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 $:

📌 Write $ -1 = e^{i\pi} $, so:

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