使用 FOIL 法展開 $$$\left(1 + 3 i\right) \left(5 + i\right)$$$

使用 FOIL 法將 $$$\left(1 + 3 i\right) \left(5 + i\right)$$$ 相乘。

$$$\left({\color{red}\left(1\right)} + {\color{purple}\left(3 i\right)}\right) \left({\color{green}\left(5\right)} + {\color{blue}\left(i\right)}\right) = \underbrace{{\color{red}\left(1\right)} {\color{green}\left(5\right)}}_{\text{第一}} + \underbrace{{\color{red}\left(1\right)} {\color{blue}\left(i\right)}}_{\text{外部}} + \underbrace{{\color{purple}\left(3 i\right)} {\color{green}\left(5\right)}}_{\text{內部}} + \underbrace{{\color{purple}\left(3 i\right)} {\color{blue}\left(i\right)}}_{\text{末頁}} = 5 + i + 15 i - 3 = 2 + 16 i$$$

$$$\left(1 + 3 i\right) \left(5 + i\right) = 2 + 16 i$$$A