Lösung 3.2:1c

By calculation, we obtain

\displaystyle \begin{align}2z+w &= 2(2+i)+(2+3i)=2\cdot 2 + 2 + (2+3)i\\ &=6+5i\end{align}

and we can mark this point on the complex plane.

If we treat \displaystyle z and \displaystyle w as vectors, then \displaystyle 2z is the vector which has the same direction as \displaystyle z, but is twice as long.

We add \displaystyle w to this vector and get \displaystyle 2z+w.