Question

find the product. write the answer in standard form.
(7 - 6i)(6 + 6i)

a. 78 + 6i
b. 6 - 78i
c. -36i² + 6i - 42
d. 78 - 6i

Explanation:

Step1: Use the distributive property (FOIL method)

Multiply each term in the first complex number by each term in the second complex number:
$$(7 - 6i)(6 + 6i)=7\times6 + 7\times6i-6i\times6-6i\times6i$$
$$= 42 + 42i-36i - 36i^{2}$$

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

Combine like terms and substitute \(i^{2}=-1\):
First, combine the \(i\) terms: \(42i-36i = 6i\)
Then, substitute \(i^{2}=-1\) into \(-36i^{2}\): \(-36\times(-1)=36\)
Now, combine the real parts: \(42 + 36=78\)
So the expression becomes \(78 + 6i\)

Answer:

A. \(78 + 6i\)