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Home » $ S(5,3) = 25 $ - AMAZONAWS

$ S(5,3) = 25 $ - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 So the six roots are:

📌 e^{2\pi i / 9},\ e^{8\pi i / 9},\ e^{14\pi i / 9},\ e^{-2\pi i / 9},\ e^{-8\pi i / 9},\ e^{4\pi i / 9}.

📌 The imaginary part of $ e^{i\theta} $ is $ \sin \theta $. We compute $ \sin \theta $ for each angle:

📌 $ \sin(2\pi/9) = \sin(40^\circ) \approx 0.6428 $

📌 $ \sin(8\pi/9) = \sin(160^\circ) = \sin(20^\circ) \approx 0.3420 $

📌 $ \sin(14\pi/9) = \sin(280^\circ) = \sin(-80^\circ) = -\sin(80^\circ) $ (negative)

📌 $ \sin(-2\pi/9) = -\sin(40^\circ) $

📌 $ \sin(-8\pi/9) = -\sin(40^\circ) $

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