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+\end{exercise} + +\begin{exercise}[subtitle={Exponentielle -> Algébrique}, step={2}, origin={Création}, topics={Exponentielle complexe}, tags={Complexe}] + \begin{multicols}{3} + \begin{enumerate} + \item $z_1 = e^{i\pi}$ + \item $z_2 = e^{-i\frac{\pi}{3}}$ + \item $z_3 = 2e^{i\frac{\pi}{4}}$ + + \item $z_4 = e^{-i\frac{\pi}{2}}$ + \item $z_5 = 5e^{-i\frac{4\pi}{3}}$ + \item $z_6 = e^{i\frac{\pi}{2}} + e^{-2i\pi}$ + + \item $z_7 = 10e^{i\frac{2\pi}{6}}$ + \item $z_8 = \frac{1}{2}e^{i\pi}$ + \item $z_9 = 56e^{-i\frac{\pi}{6}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Opération avec la forme trigonométrique}, step={2}, origin={Création}, topics={Exponentielle complexe}, tags={Complexe}] + On définit les nombres complexes suivants + \[ + z_1 = \frac{\sqrt{2}}{2} - i\frac{\sqrt{2}}{2} \qquad z_2 = 1 - i\sqrt{3} + \] + \begin{enumerate} + \item Déterminer la forme exponentielle des nombres complexes. + \item Effectuer les opérations suivantes et donner le résultat sous forme exponentielle. + \begin{multicols}{2} + \begin{enumerate} + \item $z_a = z_1 \times z_2$ + \item $z_b = \dfrac{z_1}{z_2}$ + \end{enumerate} + \end{multicols} + \item Calculer les quantités suivantes + \begin{multicols}{3} + \begin{enumerate} + \item $z_A = z_1^2$ + \item $z_B = z_1^3$ + \item $z_C = z_2^4$ + \end{enumerate} + \end{multicols} + \item Placer le résultat de ces opérations dans un repère. + \end{enumerate} +\end{exercise} \collectexercisesstop{banque} diff --git a/TST_sti2d/06_Exponentielle_complexe/index.rst b/TST_sti2d/06_Exponentielle_complexe/index.rst index 12e2e4b..faa9629 100644 --- a/TST_sti2d/06_Exponentielle_complexe/index.rst +++ b/TST_sti2d/06_Exponentielle_complexe/index.rst @@ -2,7 +2,7 @@ Exponentielle complexe ###################### :date: 2021-01-14 -:modified: 2021-01-14 +:modified: 2021-01-25 :authors: Benjamin Bertrand :tags: Complexe :category: TST_sti2d @@ -23,3 +23,18 @@ Bilan :height: 200px :alt: Bilan sur la forme complexe +Étape 2: Exercices techniques pas rigolos +========================================= + +Les élèves s'exercent avec la forme trigonométrique avec une série d'exercices techniques. + +.. image:: ./2E_techniques.pdf + :height: 200px + :alt: Exercices techniques avec la forme exponentielle + +Étape 3: Applications des nombres complexes +============================================ + +Exercices de géométrie et d'électricité utilisant les nombres complexes. + +