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Home » There is only one such number. Therefore, the arithmetic mean is simply: - Upplift

There is only one such number. Therefore, the arithmetic mean is simply: - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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\boxed{\left( -\dfrac{4}{3}, \dfrac{3}{4} \right)}
Question: The maximum imaginary part of a root of $ z^5 + z^3 + z + 1...
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...
The roots with maximum imaginary part are $ e^{i\pi/3} $ and $ e^{
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