From Förberedande kurs i matematik 2

By calculation, we obtain

\displaystyle 2z+w = 2(2+i)+(2+3i) = 2\cdot 2 + 2 + (2+3)i = 6+5i

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.