2020-11-02 14:11:43 +00:00
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\documentclass[a4paper,12pt]{article}
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\usepackage{myXsim}
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\title{Complexes, module et argument}
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\tribe{Terminale ST Sti2d}
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\date{Novembre 2020}
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\pagestyle{empty}
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\geometry{left=10mm,right=10mm, top=10mm}
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\begin{document}
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\setcounter{section}{2}
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\section{Transformations géométriques}
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\begin{bclogo}[barre=none, arrondi=0.1, logo=]{Définition}
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Des transformations géométriques peuvent être décrites avec des fonctions manipulant des nombres complexes.
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\begin{itemize}
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\item La \textbf{translation de vecteur $\vec{u} = \vectCoord{a}{b}$} est décrite par la fonction
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\[
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f : z \mapsto z + u
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\]
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où $u$ est le nombre complexe $u = a + ib$ l'affixe de $\vec{u}$.
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\begin{tikzpicture}[yscale=.8, xscale=.8]
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\repereNoGrid{-1}{4}{-1}{4}
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\draw[|->] (1,-1) node [above left] {$M$} -- (3,3) node [above right] {$M'$};
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\draw[|->] (1,1) node [above left] {$N$} -- (3,5) node [above right] {$N'$};
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\draw[|->] (-1,1) node [above left] {$L$} -- (1,5) node [above right] {$L'$};
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\end{tikzpicture}
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2020-11-04 08:38:15 +00:00
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\item \textbf{L'homothétie de centre $O$ de rapport} $k \in \R$ est décrite par la fonction
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2020-11-02 14:11:43 +00:00
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\[
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f : z \mapsto k \times z
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\]
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\begin{tikzpicture}[yscale=.8, xscale=.8]
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\repereNoGrid{-1}{4}{-1}{4}
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\draw[|->] (30:1) node [above left] {$M$} -- (30:2) node [above right] {$M'$};
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\draw[|->] (60:2) node [above left] {$N$} -- (60:4) node [above right] {$N'$};
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\draw[|->] (-30:0.5) node [below left] {$L$} -- (-30:1) node [below right] {$L'$};
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\draw[|->] (120:1) node [above left] {$P$} -- (120:2) node [above left] {$P'$};
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\end{tikzpicture}
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\end{itemize}
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\end{bclogo}
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\end{document}
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