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| -rw-r--r-- | buch/chapters/05-zahlen/images/komplex.tex | 39 |
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diff --git a/buch/chapters/05-zahlen/images/komplex.tex b/buch/chapters/05-zahlen/images/komplex.tex new file mode 100644 index 0000000..8cda85b --- /dev/null +++ b/buch/chapters/05-zahlen/images/komplex.tex @@ -0,0 +1,39 @@ +% +% komplex.tex -- Betrag und Argument einer komplexen Zahl +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1.5} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\pgfmathparse{atan(2/3)} +\xdef\winkel{\pgfmathresult} +\fill[color=blue!20] (0,0) -- (1.5,0) arc (0:\winkel:1.5) -- cycle; +\draw[->] (-1,0) -- (4,0) coordinate[label={$\Re z$}]; +\draw[->] (0,-1) -- (0,3) coordinate[label={right:$\Im z$}]; +\draw[line width=0.5pt] (3,0) -- (3,2); +\node at (3,1) [right] {$\Im z=b$}; +\node at (1.5,0) [below] {$\Re z=a$}; +\draw[->,color=red,line width=1.4pt] (0,0) -- (3,2); +\node at (3,2) [above right] {$z=a+bi$}; +\def\punkt#1{ + \fill[color=white] #1 circle[radius=0.04]; + \draw #1 circle[radius=0.04]; +} +\punkt{(0,0)} +\punkt{(3,2)} +\node[color=red] at (1.5,1) [rotate=\winkel,above] {$r=|z|$}; +\node[color=blue] at ({\winkel/2}:1.0) + [rotate={\winkel/2}] {$\varphi=\operatorname{arg}z$}; + +\end{tikzpicture} +\end{document} + |