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âNintendo Switch Leaked: This Unseen Upgrade Will Take Your Gaming to New Heights!â - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: The maximum imaginary part of a root of $ z^5 + z^3 + z + 1 = 0 $ can be expressed as $ \sin \theta $. Find $ \theta $ in degrees.

📌 Solution: Factor the polynomial:

📌 z^5 + z^3 + z + 1 = z^3(z^2 + 1) + 1(z + 1).

📌 Group terms:

📌 Roots: $ z^3 = -1 \implies z = e^{i\pi/3 + 2k\pi/3} $, and $ z^2 = -1 \implies z = e^{i\pi/2}, e^{i3\pi/2} $.

📌 The roots with maximum imaginary part are $ e^{i\pi/3} $ and $ e^{

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