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-rw-r--r--komfour_zf.tex74
1 files changed, 68 insertions, 6 deletions
diff --git a/komfour_zf.tex b/komfour_zf.tex
index fd4b33d..b9ed253 100644
--- a/komfour_zf.tex
+++ b/komfour_zf.tex
@@ -15,12 +15,20 @@
\usepackage{polyglossia}
\setdefaultlanguage[variant=swiss]{german}
+%% Math
+\usepackage{amsmath}
+\usepackage{amsthm}
+
+%% Layout
+\usepackage{multicol}
+\usepackage{enumitem}
+
%% License configuration
\usepackage[
- type={CC},
- modifier={by-nc-sa},
- version={4.0},
- lang={german},
+ type={CC},
+ modifier={by-nc-sa},
+ version={4.0},
+ lang={german},
]{doclicense}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -31,12 +39,38 @@
\semester{Fr\"uhlingssemester 2020}
\authoremail{npross@hsr.ch}
-\author{\textsl{Naoki Pross} -- \texttt{\theauthoremail}}
+\author{Naoki Pross -- \texttt{\theauthoremail}}
\title{\texttt{\themodule} Zusammenfassung}
\date{\thesemester}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Macros and settings
+
+%% Equal by definition
+\newcommand\defeq{\overset{\mathrm{def.}}{=}}
+
+%% number sets
+\newcommand\Rset{\mathbb{R}}
+\newcommand\Cset{\mathbb{C}}
+
+%% Complex operators
+\DeclareMathOperator\cjs{cjs}
+\newcommand\cjsl[1]{\cos #1 + j\sin #1}
+
+\newcommand\ej[1]{e^{j#1}}
+\newcommand\conj[1]{\overline{j #1}}
+
+\renewcommand\Re{Re}
+\renewcommand\Im{Im}
+
+%% Theorems
+\newtheorem{theorem}{Satz}
+\setlist[description]{%
+ align=right, labelwidth=2cm, leftmargin=!, %
+ format={\normalfont\slshape}}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Document
\begin{document}
@@ -45,9 +79,37 @@
\tableofcontents
\section{Komplexe Zahlen}
+\begin{theorem}[Komplexe Einheit]
+\(
+ j \defeq +\sqrt{-1} \iff j^2 = -1
+\)
+\end{theorem}
+\begin{theorem}[Multiplikation] \(a, b \in \Cset\) \(\arg a = \phi, \arg b = \theta\)
+\begin{description}
+ \item[Kartesich] \(a \odot b = (a_1 b_1 - a_2 b_2) + j (a_1 b_2 + a_2 b_1)\)
+ \item[Polar] \(a\odot b &= |a|\cdot|b|\exp{j(\phi + \theta)}\)
+\end{description}
+\end{theorem}
+\begin{theorem}[Division] \(a, b \in \Cset\) \(\arg a = \phi, \arg b = \theta\)
+\begin{description}
+ \item[Kartesich]
+ \item[Polar] \(a / b &= |a|/|b|\exp{j(\phi - \theta)}\)
+\end{description}
+\end{theorem}
+
+
+\subsection{Algebra}
+Seien \(a, b \in \Cset\) und \(a = a_1 + ja_2, a_1,a_2 \in \Rset\) und \"ahnlich f\"ur \(b\)
+\begin{align*}
+ a \oplus b &= (a_1 + b_1) + j (a_2 + b_2) \\
+\end{align*}
+
+\subsection{Neue Operationen}
+\subsection{Graphische Darstellung}
+\subsubsection{Ebene Geometrie}
\section{Lizenz}
\doclicenseThis
-
\end{document}
+% vim: set et ts=2 sw=2 spelllang=de spell wrap linebreak :