Multiplying Complex Numbers

Example:

Multiply the two complex numbers $3+5i$ and $2+4i$ .

$\begin{array}{l}\left(3+5i\right)\left(2+4i\right)=\left(3\right)\left(2\right)+\left(3\right)\left(4i\right)+\left(5i\right)\left(2\right)+\left(5i\right)\left(4i\right)\\ =6+12i+10i+20i^2\\ =6+22i+20\left(-1\right)\\ =-14+22i\end{array}$

The product is $-14+22i$ .