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Home » \(200 = \fracn2(5 + 45) = \fracn2(50)\). - ECD Germany

\(200 = \fracn2(5 + 45) = \fracn2(50)\). - ECD Germany

📅 May 8, 2026 👤 scraface

May 08, 2026

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📌 z = e^{-2\pi i / 9},\ e^{-8\pi i / 9},\ e^{-14\pi i / 9} = e^{4\pi i / 9} \quad \text{(since } -14\pi/9 \equiv 4\pi/9 \mod 2\pi).

📌 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) $

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