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hilton homewood suites san diego liberty station - ECD Germany

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 w^2 - w + 1 = 0 \implies w = \frac{1 \pm \sqrt{1 - 4}}{2} = \frac{1 \pm i\sqrt{3}}{2}

📌 إذن، $z^2 = \frac{1 \pm i\sqrt{3}}{2}$. الجذور التربيعية لـ $\frac{1 + i\sqrt{3}}{2}$ (التي تُعتبر $e^{i\pi/3}$) هي:

📌 z = e^{i\pi/6} \quad \text{و} \quad z = e^{i5\pi/6}

📌 الأجزاء التخيلية هي $\sin \frac{\pi}{6} = \frac{1}{2}$ و $\sin \frac{5\pi}{6} = \frac{1}{2}$. للجذور من $z^2 = \frac{1 - i\sqrt{3}}{2} = e^{-i\pi/3}$, فإن الجذور التربيعية هي:

📌 z = e^{-i\pi/6} \quad \text{و} \quad z = e^{-i5\pi/6}

📌 الأجزاء التخيلية هي $-\frac{1}{2}$ و $-\frac{1}{2}$ على التوالي.لذلك، الجزء التخيلي الأكبر هو $\frac{1}{2} = \sin 30^\circ$.

📌 الإجابة النهائية:** $\boxed{30^\circ}$

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