TeX Quellcode:

\begin{array}{rclll}\dfrac{x^2}{i}+\dfrac{5x\cdot i^{i+1}}{i^i}-7i &=& 0 \\\\\dfrac{x^2}{i}+5x\cdot i^{i+1-i}-7i &=& 0 &\vert & \cdot i\\\\x^2+5xi^2-7i^2 &=& 0 &\vert & i^2=-1\\x^2-5x+7 &=& 0 &\vert & \text{p-q-Formel} \\x_{1,2} &=& \dfrac{5}{2}\pm\sqrt{\left(\dfrac{5}{2}\right)^2-7}\\&=& \dfrac{5}{2}\pm\sqrt{-\dfrac{3}{4}}\\&=& \dfrac{5\pm\sqrt{-3}}{2}\\&=& \dfrac{5\pm\sqrt{-1\cdot 3}}{2} &\vert& \sqrt{-1}=i \\\\x_1 &=& \dfrac{5+\sqrt{3}\cdot i}{2}\\x_1 &=& \dfrac{5-\sqrt{3}\cdot i}{2}\\\mathbb{L} &=& \left\{\dfrac{5+\sqrt{3}\cdot i}{2}\; ; \; \dfrac{5-\sqrt{3}\cdot i}{2} \right\}\end{array}