%
% forts.tex -- analytische Fortsetzung
%
% (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,calc}
\begin{document}
\def\skala{1}
\begin{tikzpicture}[>=latex,thick,scale=\skala]

\pgfmathparse{-(3+3*sin(180*(1.4))-(1.4))}
\xdef\X{\pgfmathresult}
\pgfmathparse{-(2+2*cos(180*(1.4))-(1.4))}
\xdef\Y{\pgfmathresult}

\def\kurve#1{
	({3+3*sin(180*(#1))-(#1)+\X},{2+2*cos(180*(#1))-(#1)+\Y})
}

\def\punkt#1{
	\fill[color=white]
		({3+3*sin(180*(#1))-(#1)+\X},{2+2*cos(180*(#1))-(#1)+\Y})
		circle[radius=0.08];
	\draw[color=red]
		({3+3*sin(180*(#1))-(#1)+\X},{2+2*cos(180*(#1))-(#1)+\Y})
		circle[radius=0.08];
}

\def\kreis#1#2{
	\fill[color=gray!50,opacity=0.5] #1 circle[radius=#2];
}
\def\rand#1#2{
	\draw #1 circle[radius=#2];
}

\kreis{\kurve{-0.2}}{1.2}
\kreis{\kurve{0.0}}{1.2}
\kreis{\kurve{0.2}}{1.2}
\kreis{\kurve{0.4}}{1.2}
\kreis{\kurve{0.6}}{1.2}
\kreis{\kurve{0.8}}{1.3}
\kreis{\kurve{1.0}}{1.5}
\kreis{\kurve{1.2}}{1.3}
\kreis{\kurve{1.4}}{1.2}
\rand{\kurve{-0.2}}{1.2}
\rand{\kurve{0.0}}{1.2}
\rand{\kurve{0.2}}{1.2}
\rand{\kurve{0.4}}{1.2}
\rand{\kurve{0.6}}{1.2}
\rand{\kurve{0.8}}{1.3}
\rand{\kurve{1.0}}{1.5}
\rand{\kurve{1.2}}{1.3}
\rand{\kurve{1.4}}{1.2}

\draw[->] (-1.5,0) -- (8.5,0) coordinate[label={$\operatorname{Re}z$}];
\draw[->] (0,-2.6) -- (0,5.6) coordinate[label={left:$\operatorname{Im}z$}];

\draw[color=red,line width=1.4pt]
	plot[domain=-0.2:1.4,samples=100] 
	({3+3*sin(180*\x)-\x+\X},{2+2*cos(180*\x)-\x+\Y});

\foreach \t in {-0.2,0,0.2,0.4,0.6,0.8,1.0,1.2,1.4}{
	\punkt{\t}
}

\node[color=red] at \kurve{1.4} [above left] {$z_0$};
\node[color=red] at \kurve{1.2} [below] {$z_1$};
\node[color=red] at \kurve{1.0} [below] {$z_2$};
\node[color=red] at \kurve{0.8} [below right] {$z_3$};
\node[color=red] at \kurve{0.6} [right] {$z_4$};
\node[color=red] at \kurve{0.4} [right] {$z_5$};
\node[color=red] at \kurve{0.2} [above right] {$z_6$};
\node[color=red] at \kurve{0.0} [above] {$z_7$};
\node[color=red] at \kurve{-0.2} [above left] {$z_8$};

\node[color=red] at \kurve{0.96} [above] {$\gamma$};

\end{tikzpicture}
\end{document}

