the table shows several complex numbers where / is the imaginary unit. select all appropriate cells in the table where the product of the two numbers is a real number.

Question

Accepted Answer

# Explanation:
## Step1: Multiply $8 + 2i$ and $8 - 2i$
Use the formula $(a+bi)(a - bi)=a^{2}+b^{2}$. Here $a = 8$ and $b=2$.
$$
\begin{align*}
(8 + 2i)(8 - 2i)&=8^{2}-(2i)^{2}\
&=64-4i^{2}\
&=64 + 4\
&=68
\end{align*}
$$
## Step2: Multiply $5i$ and $i$
Use the property $i^{2}=-1$.
$$
\begin{align*}
5i\times i&=5i^{2}\
&=- 5
\end{align*}
$$
## Step3: Multiply $-4$ and $3$
$$
-4\times3=-12
$$

# Answer:
The cells corresponding to $(8 + 2i)\times(8 - 2i)$, $5i\times i$, $-4\times3$ should be selected.

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QUESTION IMAGE

Question

Explanation:

Step1: Multiply \(8 + 2i\) and \(8 - 2i\)

Step2: Multiply \(5i\) and \(i\)

Step3: Multiply \(-4\) and \(3\)

Answer: