Hammond Mills
03/22/2024 · High School
Exercice 1: D. Ecrirc sous forme trigonométrique : \( z_{1}=2\left(\cos \frac{\pi}{4}-i \sin \frac{\pi}{4}\right) \) \( \begin{array}{ll}z_{2}=-3\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right) \quad z_{3}=2\left(\cos \frac{\pi}{4}+i \sin \frac{3 \pi}{4}\right) \\ z_{4}=\cos \frac{\pi}{6}+i \sin \left(-\frac{\pi}{6}\right) \quad z_{5}=\cos \theta-i \sin \theta \quad z_{5}=\sin \theta+i \cos \theta\end{array} \)
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**Exercice 1 : Partie D. Écrire sous forme trigonométrique**
1. \( z_{1} = 2 \left( \cos \frac{7\pi}{4} + i \sin \frac{7\pi}{4} \right) \)
2. \( z_{2} = 3 \left( \cos \frac{5\pi}{3} + i \sin \frac{5\pi}{3} \right) \)
3. \( z_{3} = 2 \left( \cos \frac{\pi}{4} + i \sin \frac{3\pi}{4} \right) \) (Vérification recommandée)
4. \( z_{4} = \cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6} \)
5. \( z_{5} = \cos (2\pi - \theta) + i \sin (2\pi - \theta) \)
6. \( z_{6} = \cos \left(\frac{\pi}{2} - \theta\right) + i \sin \left(\frac{\pi}{2} - \theta\right) \)
*Remarque :* Pour \( z_{3} \), assurez-vous que les angles des fonctions cosinus et sinus sont corrects pour une forme trigonométrique standard.
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