=for timestamp
Di Nov 23 15:59:49 CET 2004

=head2 Hausaufgaben

=head3 1. Hausaufgabe

=head4 Buch Seite 25, Aufgabe 1

=over

=item a)

Berechne M<\mathrm{i}^n> für M<n \in \left\{ 2, 3, 4, \ldots, 9, 32, 33, 34, 35
\right\}>!

=item b)

Berechne M<\mathrm{i}^{4n}>, M<\mathrm{i}^{4n + 1}>, M<\mathrm{i}^{4n + 2}>,
M<\mathrm{i}^{4n + 3}>, wenn M<n \in \mathds{N}> ist!

=over

=item *

M<\mathrm{i}^{4n} = \mathrm{i}^4 = \mathrm{i}^8 = \mathrm{i}^{32} = 1;>

=item *

M<\mathrm{i}^{4n + 1} = \mathrm{i}^9 = \mathrm{i}^5 = \mathrm{i}^9 = \mathrm{i}^{33} = \mathrm{i};>

=item *

M<\mathrm{i}^{4n + 2} = \mathrm{i}^2 = \mathrm{i}^6 = \mathrm{i}^{34} = -1;>

=item *

M<\mathrm{i}^{4n + 3} = \mathrm{i}^3 = \mathrm{i}^7 = \mathrm{i}^{35} = -\mathrm{i};>

=back

=item c)

Berechne M<\left(-\mathrm{i}\right)^{4n}>, M<\left(-\mathrm{i}\right)^{4n+1}>,
M<\left(-\mathrm{i}\right)^{4n+2}>, M<\left(-\mathrm{i}\right)^{4n+3}> für M<n
\in \mathds{N}>!

=over

=item *

M<\left(-\mathrm{i}\right)^{4n} = 1;>

=item *

M<\left(-\mathrm{i}\right)^{4n + 1} = -\mathrm{i};>

=item *

M<\left(-\mathrm{i}\right)^{4n + 2} = -1;>

=item *

M<\left(-\mathrm{i}\right)^{4n + 3} = \mathrm{i};>

=back

=back