Hallo,
erweitere konjugiert komplex:
\( \begin{aligned} \frac{z+1}{z-1} &=\frac{x+i y+1}{x+i y-1} \cdot \frac{x-1-i y}{x-1-i y} \\ &=\frac{x^{2}+y^{2}-2iy-1}{x^{2}-2 x+y^{2}+1} \\ &=\frac{x^{2}+y^{2}-1}{x^{2}+y^{2}-2 x+1}+i \frac{-2 y}{x^{2}+y^{2}-2 x+1} \end{aligned} \)
\( \operatorname{Re}\left(\frac{z+1}{z-1}\right)=\frac{x^{2}+y^{2}-1}{x^{2}+y^{2}-2 x+1} \)
\( lm\left(\frac{z+1}{z-1}\right)=\frac{-2 y}{x^{2}+y^{2}-2 x+1} \)
