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diff --git a/TST_sti2d/03_Complexes/3B_transformations.tex b/TST_sti2d/03_Complexes/3B_transformations.tex index c785ff9..f5599d2 100644 --- a/TST_sti2d/03_Complexes/3B_transformations.tex +++ b/TST_sti2d/03_Complexes/3B_transformations.tex @@ -29,7 +29,7 @@ \draw[|->] (-1,1) node [above left] {$L$} -- (1,5) node [above right] {$L'$}; \end{tikzpicture} - \item \textbf{L'homothétie de rapport} $k \in \R$ est décrite par la fonction + \item \textbf{L'homothétie de centre $O$ de rapport} $k \in \R$ est décrite par la fonction \[ f : z \mapsto k \times z \] diff --git a/TST_sti2d/03_Complexes/3E_transformations.pdf b/TST_sti2d/03_Complexes/3E_transformations.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b6e733525d69f0f4d48540ae00914be011910280 GIT binary patch literal 86188 zcmce+W3VXQvL(7~+qP}n)?T)4+qP}nwy~FO+g5+4``(Uz@m|F1Kj&0LO=iuiQ6nQ~ zX5=JQ5D}wgq+^95{kt@>2E{_aKwxKR3B|($MX%yvZ$dz?A#Z4DV&n`(uk2#z{69y; 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+\documentclass[a4paper,landscape,twocolumn,10pt]{article} \usepackage{myXsim} \author{Benjamin Bertrand} \title{Complexes - Cours} -\date{Octobre 2020} +\date{Novembre 2020} \DeclareExerciseCollection{banque} \xsimsetup{ - step=2, + step=3, } \setlength{\columnseprule}{0pt} diff --git a/TST_sti2d/03_Complexes/exercises.tex b/TST_sti2d/03_Complexes/exercises.tex index f79a0c5..e79781e 100644 --- a/TST_sti2d/03_Complexes/exercises.tex +++ b/TST_sti2d/03_Complexes/exercises.tex @@ -107,4 +107,52 @@ \end{multicols} \end{exercise} +\begin{exercise}[subtitle={Fonctions complexes}, step={3}, origin={Création}, topics={Complexes}, tags={Complexes, Fonctions}] + Dans cet exercice, on étudie des fonctions qui manipulent des nombres complexes. On étudiera leurs effets géométriques à partir des points $A$, $B$, $C$ et $D$ définit par les nombres complexes suivants + \[ + z_A = 1 + i \qquad + z_B = 1 - 2i \qquad + z_C = -3 + i \qquad + z_D = 2 - i + \] + \begin{enumerate} + \item Tracer le plan complexe et placer les points. + \item On définit la fonction $f(z) = z + 2i + 1$ + \begin{enumerate} + \item Calculer $z_{A'} = f(z_A)$ puis placer en rouge la point $A'$ sur le plan complexe. + \item Faire la même chose pour $z_B$, $z_C$ et $z_D$. + \item Décrire l'effet géométrique de la fonction $f$. + \end{enumerate} + \item On définit la fonction $g(z) = z - i + 2$ + \begin{enumerate} + \item Calculer $z_{A''} = g(z_A)$ puis placer en noir la point $A''$ sur le plan complexe. + \item Faire la même chose pour $z_B$, $z_C$ et $z_D$. + \item Décrire l'effet géométrique de la fonction $g$. + \end{enumerate} + \item On définit la fonction $h(z) = 2z$ + \begin{enumerate} + \item Calculer $z_{A'''} = g(z_A)$ puis placer en vert la point $A'''$ sur le plan complexe. + \item Faire la même chose pour $z_B$, $z_C$ et $z_D$. + \item Décrire l'effet géométrique de la fonction $h$. + \end{enumerate} + \item(*) On définit la fonction $j(z) = iz$ + \begin{enumerate} + \item Calculer $z_{A""} = g(z_A)$ puis placer en vert la point $A""$ sur le plan complexe. + \item Faire la même chose pour $z_B$, $z_C$ et $z_D$. + \item Décrire l'effet géométrique de la fonction $j$. + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Transformations du plan complexe}, step={3}, origin={Création}, topics={Complexes}, tags={Complexes, Fonctions}] + Écrire la fonction complexe qui permet de réaliser les transformations suivantes + \begin{enumerate} + \item La translation de 2 unités à droite et 1 unité en bas. + \item La translation de vecteur $\vec{v} = \vectCoord{-2}{-5}$. + \item L'homothétie de rapport 5. + \item L'homothétie de rapport 0.1. + \end{enumerate} +\end{exercise} + + \collectexercisesstop{banque} diff --git a/TST_sti2d/03_Complexes/index.rst b/TST_sti2d/03_Complexes/index.rst index c805005..f86e63c 100644 --- a/TST_sti2d/03_Complexes/index.rst +++ b/TST_sti2d/03_Complexes/index.rst @@ -2,7 +2,7 @@ Complexes ######### :date: 2020-09-29 -:modified: 2020-10-08 +:modified: 2020-11-04 :authors: Benjamin Bertrand :tags: Complexes, Trigonométrie :category: TST_sti2d @@ -36,12 +36,27 @@ Cours: Définition de la notation trigonométrique. Passage de la forme algébri Exercices techniques pour le passage d'une forme à l'autre avec toujours le lien avec le plan complexe. +.. image:: ./2E_forme_trigo.pdf + :height: 200px + :alt: Calculs techniques sur la forme trigonométrique. + Étape 3: Transformation géométriques ==================================== Les trois transformations au programme. Les élèves calculent les images de points par ces transformations et en conclue sur l'effet géométrique de ces transformations. -Cours: les 3 transformations. +.. image:: ./3E_transformations.pdf + :height: 200px + :alt: Découverte des transformations du plan complexe + +Cours: les 2 transformations la translation et l'homothétie. + +.. image:: ./3B_transformations.pdf + :height: 200px + :alt: Cours sur les translations et les homothéties. + + + Étape 4: Équations géométriques ===============================