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26 lines
1.1 KiB
TeX
26 lines
1.1 KiB
TeX
\begin{tikzpicture}[scale=3]
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\tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
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\tkzSetUpLine[line width=1]
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\tkzInit[xmax=1.2,ymax=1,xmin=-1.2,ymin=0]
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\pgfmathsetmacro{\Radius}{1}
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\tkzDefPoints{2.0/1.0/Z, 0/0/O, 0/1/i}
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%% Konstruktion von 1/ \overline{z} und -1/ \overline{z}
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\tkzTangent[from with R = Z,/tikz/overlay](O,\Radius cm) \tkzGetPoints{T1}{T2}
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\tkzInterLL(T1,T2)(O,Z) \tkzGetPoint{dZ}
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\tkzDefPointBy[reflection = over O--i](dZ) \tkzGetPoint{ndZ}
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\tkzDefPointBy[symmetry = center O](dZ) \tkzGetPoint{other}
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%%
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\tkzDrawArc[R,line width=1pt,color=orange](O,\Radius cm)(0,180)
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\tkzAxeXY
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\tkzDrawPoints(Z, dZ, ndZ, other)
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\tkzLabelPoint[left](Z){$z = r \cdot e^{\iu \varphi}$}
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\tkzLabelPoint[below](other){$-\frac{1}{\overline{z}}$}
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\tkzLabelPoint[below right](dZ){$\frac{1}{\overline{z}} = \frac{1}{r} \cdot e^{\iu \varphi}$}
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\tkzLabelPoint[above left](ndZ){?}
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\tkzDrawSegments[dashed](O,Z)
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\tkzDrawSegments[dashed](O,ndZ)
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\tkzDrawSegments[dashed](O,other)
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\end{tikzpicture}
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