Lösung 3.1:1e

A suitable first step can be to work out the square term, \displaystyle (2-i)^2, with the help of the square rule:

\displaystyle \begin{align}(2-i)^2&=2^2-2\cdot 2i + i^2=4-4i+i^2\\ &=4-4i-1=3-4i\end{align}

After that, we calculate the remaining product:

\displaystyle \begin{align}(1+i)(3-4i)&=1\cdot3-1\cdot 4i +i \cdot 3 - i\cdot 4i\\ &=3-4i+3i-4i^2\\ &=3+(-4+3)i-4\cdot (-1)\\ &=3-i+4\\ &=7-i.\end{align}