Question

what real numbers should go in the boxes below when expressing the product of (-3 + 8i) and (6 + 2i) in a+bi form? (-3 + 8i)(6 + 2i)=□+□i

Explanation:

Step1: Expand the product using FOIL method

\[

$$\begin{align*} (-3 + 8i)(6+2i)&=-3\times6+(-3)\times(2i)+8i\times6 + 8i\times(2i)\\ &=-18-6i + 48i+16i^{2} \end{align*}$$

\]

Step2: Recall that \(i^{2}=-1\)

\[

$$\begin{align*} -18-6i + 48i+16i^{2}&=-18-6i + 48i+16\times(-1)\\ &=-18-16+( - 6i+48i)\\ &=-34 + 42i \end{align*}$$

\]

Answer:

-34, 42