Lösung.

Es gilt

$ \mbox{$\displaystyle \begin{array}{rcl} \mathrm{i}^{2\mathrm{i}} & = & \exp(... ...mathrm{i}(\mathrm{i}\frac{\pi}{2})) \\ & = & \exp(-{\pi}). \\ \end{array}$}$
Damit folgt $ \mbox{${\operatorname{Log}}(\mathrm{i}^{2\mathrm{i}}) = {\operatorname{Log}}(\exp(-\pi)) = -\pi$}$.

Es gilt

$ \mbox{$\displaystyle \begin{array}{rcl} {\operatorname{Log}}(1+\mathrm{i}\sqr... ...frac{\pi}{3}))) \\ & = & \log 2 + \mathrm{i}\frac{\pi}{3}. \\ \end{array}$}$