Plot polar points and interpret a complex multiplier

Place $z_1$ at radius 4 and angle 60° in quadrant I, and $z_2$ at radius 2 and angle −30° in quadrant IV. Their Cartesian forms are $z_1=2+2\sqrt3\,i$ and $z_2=\sqrt3-i$. The angle between the rays is $\pi/3-(-\pi/6)=\pi/2$, so the triangle is right-angled at $O$. Hence $|z_1-z_2|=\sqrt{4^2+2^2}=\sqrt{20}=2\sqrt5$.

The multiplier has modulus $4/2=2$ and argument $\pi/3-(-\pi/6)=\pi/2$, so $a=2i$. Starting from the point for $z_2$, rotate 90° anticlockwise about $O$, then enlarge by scale factor 2 about $O$ to reach the point for $z_1$. Indeed $2i(\sqrt3-i)=2+2\sqrt3\,i$.