TeX Quellcode:

\begin{array}{rcl}z_0 &=& \sqrt[4]{\dfrac{1}{2}}\cdot\left(\cos\left(\genfrac{}{}{1pt}{0}{\frac{2\pi}{3}+2\cdot 0\cdot\pi}{4}\right)+i\sin\left(\genfrac{}{}{1pt}{0}{\frac{2\pi}{3}+2\cdot 0\cdot\pi}{4}\right)\right) \\&=& \sqrt[4]{\dfrac{1}{2}}\cdot\left(\cos\left(\dfrac{\pi}{6}\right)+i\sin\left(\dfrac{\pi}{6}\right)\right) \\&=& \dfrac{1}{\sqrt[4]{2}}\cdot\left(\dfrac{\sqrt{3}}{2}+i\dfrac{1}{2}\right) \\&=& \dfrac{\sqrt{3}}{2\sqrt[4]{2}}+\dfrac{1}{2\sqrt[4]{2}}i \\\\z_1 &=& \sqrt[4]{\dfrac{1}{2}}\cdot\left(\cos\left(\genfrac{}{}{1pt}{0}{\frac{2\pi}{3}+2\cdot 1\cdot\pi}{4}\right)+i\sin\left(\genfrac{}{}{1pt}{0}{\frac{2\pi}{3}+2\cdot 1\cdot\pi}{4}\right)\right) \\&=& \sqrt[4]{\dfrac{1}{2}}\cdot\left(\cos\left(\dfrac{2\pi}{3}\right)+i\sin\left(\dfrac{2\pi}{3}\right)\right) \\&=& \dfrac{1}{\sqrt[4]{2}}\cdot\left(-\dfrac{1}{2}+i\dfrac{\sqrt{3}}{2}\right) \\&=& -\dfrac{1}{2\sqrt[4]{2}}+\dfrac{\sqrt{3}}{2\sqrt[4]{2}}i \end{array}