(related to Proposition: Multiplication of Complex Numbers Using Polar Coordinates)
$$\begin{array}{rcl}z\cdot w&=&r\exp(i\phi)\cdot s\exp(i\psi)\\ &=&r(\cos(\phi)+i\sin(\phi))\cdot s(\cos(\psi)+i\sin(\psi))\\ &=& (r\cdot s)\cdot [\cos(\phi)\cdot\cos(\psi)+i\sin(\phi)\cdot\sin(\psi) + i\sin(\psi)\cos(\phi)-\sin(\phi)\sin(\psi)]\\ &=& (r\cdot s)\cdot [\cos(\phi+\psi)+i\sin(\phi+\psi)]. \end{array}$$
