simplify.
(3 + 8i)(10 + 10i)
write your answer in the form a + bi.

Question

Accepted Answer

# Explanation:
## Step1: Use the distributive property (FOIL method)
We multiply each term in the first complex number by each term in the second complex number:
$$
\begin{align*}
(3 + 8i)(10 + 10i)&=3\times10+3\times10i + 8i\times10+8i\times10i\
&= 30+30i+80i + 80i^{2}
\end{align*}
$$
## Step2: Recall that $i^{2}=- 1$
Substitute $i^{2}=-1$ into the expression:
$$
\begin{align*}
30+30i + 80i+80\times(-1)&=30+30i+80i - 80\
&=(30 - 80)+(30i+80i)
\end{align*}
$$
## Step3: Combine like terms
Combine the real parts and the imaginary parts separately:
$$
\begin{align*}
(30 - 80)+(30i + 80i)&=-50 + 110i
\end{align*}
$$
# Answer:
$-50 + 110i$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the distributive property (FOIL method)

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

Step3: Combine like terms

Answer: