=for timestamp
Di Feb 15 16:00:29 CET 2005

=head3 10. Hausaufgabe

=head4 Selbstgestellte Aufgabe

M<z_1 = -1 + \mathrm{i}\sqrt{3} = 2E(\frac{2}{3}\pi);>

M<z_2 = 4E(\frac{11}{6}\pi);>

⇒ M<z_1z_2 = 8E(\frac{2}{3}\pi + \frac{11}{6}\pi) = 8E(\frac{5}{2}\pi) =
8E(\frac{\pi}{4}) = 8\mathrm{i};>

⇒ M<\frac{z_1}{z_2} = \frac{1}{2}E(\frac{2}{3}\pi - \frac{11}{6}\pi) =
\frac{1}{2}E(-\frac{7}{6}\pi) = \frac{1}{2}E(\frac{5}{6}\pi) =
-\frac{1}{4}\sqrt{3} + \frac{1}{4}\mathrm{i};>

⇒ M<z_1^{-1} = \frac{E(0)}{z_1} = \frac{1}{2}E(-\frac{2}{3}\pi) =
\frac{1}{2}E(\frac{4}{3}\pi) = -\frac{1}{4} - \frac{1}{4}\sqrt{3}\mathrm{i};>

⇒ M<z_2^{-1} = \frac{E(0)}{z_2} = \frac{1}{4}E(-\frac{11}{6}\pi) =
\frac{1}{4}E(\frac{\pi}{6}) = \frac{1}{8}\sqrt{3} + \frac{1}{8}\mathrm{i};>