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

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. \(63 + 22i\)