Lösung.

$ \mbox{${\operatorname{Log}}(\mathrm{i}) = \mathrm{i}\frac{\pi}{2}$}$.
$ \mbox{${\operatorname{Log}}(-\frac{1}{2}\sqrt{2} + \frac{\mathrm{i}}{2}\sqrt{2}) = \mathrm{i}\frac{3\pi}{4}$}$.
$ \mbox{${\operatorname{Log}}( \mathrm{i}(-\frac{1}{2}\sqrt{2} + \frac{\mathrm{i}}{2}\sqrt{2})) = -\mathrm{i}\frac{3\pi}{4}$}$.
Es fällt auf, daß hier $ \mbox{${\operatorname{Log}}(zw) \neq {\operatorname{Log}}(z) + {\operatorname{Log}}(w)$}$ gilt.