Question

Find the product of (2 + 2i) and (3 - 5i).

Answer 1

To multiply to complex numbers, we are going to use FOIL methos and combine like terms:

`\begin{gathered} (a+bi)(c+di)=ac+\text{adi}+\text{bci}+bdi^2 \\ =ac+(ad+bc)i-bd \\ i^2=-1\text{ -> Remember} \\ =(ac-bd)+(ad+bc)i \end{gathered}`

For this case:

`\begin{gathered} (2+2i)(3-5i)=6+-10i+6i-10i^2 \\ =6-(10-6)i+10 \\ =-4i+16 \end{gathered}`