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Home » 2\sin z \cos z = \cos z. - Coaching Toolbox

2\sin z \cos z = \cos z. - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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Question: Among all the roots of \(z^8 + z^4 + 1 = 0\), the maximum im...
Consider the equation:
z^8 + z^4 + 1 = 0
Let \(w = z^4\), then:
w = \frac{-1 \pm \sqrt{1 - 4}}{2} = \frac{-1 \pm \sqrt{-3}}{2} = \frac...
So \(z^4 = \frac{-1 \pm i\sqrt{3}}{2} = e^{\pm 2\pi i/3}\), since thes...
Thus, the solutions for \(z\) are the 4th roots of \(e^{2\pi i/3}\)
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