question 8 of 10
multiply the following complex numbers:
(5 + 3i)(4 + 2i)
a. 26 - 22i
b. 14 + 22i
c. 26 + 22i
d. 14 - 22i

Question

Accepted Answer

# Explanation:
## Step1: Use the distributive property (FOIL method)
To multiply two complex numbers $(a + bi)(c + di)$, we use the distributive property (FOIL):
$$
\begin{align*}
(5 + 3i)(4 + 2i)&=5\times4 + 5\times2i + 3i\times4 + 3i\times2i\
&=20 + 10i + 12i + 6i^2
\end{align*}
$$
## Step2: Simplify using $i^2 = -1$
Recall that $i^2 = -1$, so we substitute $i^2$ with $-1$ in the expression:
$$
\begin{align*}
20 + 10i + 12i + 6i^2&=20 + 10i + 12i + 6\times(-1)\
&=20 + 10i + 12i - 6
\end{align*}
$$
## Step3: Combine like terms
Combine the real parts and the imaginary parts separately:
$$
\begin{align*}
(20 - 6) + (10i + 12i)&=14 + 22i
\end{align*}
$$
# Answer:
B. $14 + 22i$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the distributive property (FOIL method)

Step2: Simplify using \(i^2 = -1\)

Step3: Combine like terms

Answer: