To solve the expression [tex]\((8 - 3i) - (8 - 3i)(8 + 8i)\)[/tex], let's go through the steps in detail.
1. Calculate [tex]\((8 - 3i)(8 + 8i)\)[/tex]:
- Use the distributive property (also known as FOIL for binomials): [tex]\((a + bi)(c + di) = ac + adi + bci + bdi^2\)[/tex].
- For the given expression:
[tex]\[(8 - 3i)(8 + 8i)\][/tex]
[tex]\[
= 8 \cdot 8 + 8 \cdot 8i - 3i \cdot 8 - 3i \cdot 8i
\][/tex]
- Calculate each component:
[tex]\[
= 64 + 64i - 24i - 24i^2
\][/tex]
[tex]\[
= 64 + 64i - 24i - 24(-1) \quad \text{(since } i^2 = -1 \text{)}
\][/tex]
[tex]\[
= 64 + 64i - 24i + 24
\][/tex]
[tex]\[
= (64 + 24) + (64i - 24i)
\][/tex]
[tex]\[
= 88 + 40i
\][/tex]
2. Subtract [tex]\((8 - 3i)\)[/tex] from the result obtained:
[tex]\[
(8 - 3i) - (88 + 40i)
\][/tex]
- Separate the real and imaginary parts:
[tex]\[
= (8 - 88) + (-3i - 40i)
\][/tex]
[tex]\[
= -80 - 43i
\][/tex]
Thus, the value of the expression [tex]\((8 - 3i) - (8 - 3i)(8 + 8i)\)[/tex] is [tex]\(-80 - 43i\)[/tex].
The correct answer is:
B. [tex]\(-80 - 43i\)[/tex]
