Hallo,
erweitert den Bruch mit dem konjugiert Komplexen des Nenners.
\( \dfrac{(1+i)(2+3 i)(4-2 i)}{(1+2 i)^{2}(1-i)} \)
\(= \dfrac{(1+i)(2+3 i)(4-2 i)(1-2 i)^{2}(1+i)}{(1+2 i)^{2}(1-2 i)^{2}(1-i)(1+i)} \)
\( =\dfrac{(2-3+2i+3i)(4+2+4i-2 i)(1-4-4i)}{25\cdot2} \)
\( =\dfrac{1}{50}\cdot(-1+5i)(6+2 i)(-3-4 i) \)
\( =\dfrac{1}{50}\cdot(-16+28i)(-3-4 i) \)
\( =\dfrac{1}{50}\cdot(48+112+64i-84i) \)
\( =\dfrac{160-20i}{50} \)
\( =3.2-0.4 i \)
:-)
