question 5 of 10
multiply the following complex numbers:
(8 - 3i)(6 + 5i)

a. 63 - 22i
b. 63 + 22i
c. 33 - 22i
d. 33 + 22i

Question

question 5 of 10
multiply the following complex numbers:
(8 - 3i)(6 + 5i)

a. 63 - 22i
b. 63 + 22i
c. 33 - 22i
d. 33 + 22i

Accepted Answer

# Explanation:
## Step1: Apply the distributive property (FOIL method)
Multiply each term in the first complex number by each term in the second complex number:
$$
\begin{align*}
(8 - 3i)(6 + 5i)&= 8\times6 + 8\times5i - 3i\times6 - 3i\times5i\
&= 48 + 40i - 18i - 15i^2
\end{align*}
$$
## Step2: Simplify using $i^2 = -1$
Simplify the $i^2$ term and combine like terms:
$$
\begin{align*}
&48 + 40i - 18i - 15\times(-1)\
&= 48 + 40i - 18i + 15\
&= (48 + 15) + (40i - 18i)\
&= 63 + 22i
\end{align*}
$$
# Answer:
B. $63 + 22i$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Apply the distributive property (FOIL method)

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

Answer: