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Home » \( 3n^2 + 7n - 220 = 0 \) - AMAZONAWS

\( 3n^2 + 7n - 220 = 0 \) - 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},\...
The imaginary part of $ e^{i\theta} $ is $ \sin \theta $. We compute $...
$ \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)...
$ \sin(-2\pi/9) = -\sin(40^\circ) $
$ \sin(-8\pi/9) = -\sin(40^\circ) $
$ \sin(4\pi/9) = \sin(80^\circ) \approx 0.9848 $
The maximum imaginary part is $ \sin(4\pi/9) = \sin(80^\circ) $.

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