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What is the value of the expression given below?
[tex]\[ (8 - 3i) - (8 - 3i)(8 + 8i) \][/tex]

A. [tex]\(-80 - 43i\)[/tex]

B. [tex]\(-96 + 37i\)[/tex]

C. [tex]\(-80 + 43i\)[/tex]

D. [tex]\(-96 - 37i\)[/tex]

Sagot :

GinnyAnswer
To solve the expression [tex]\((8 - 3i) - (8 - 3i)(8 + 8i)\)[/tex], we will simplify the components step-by-step.

First, compute the product [tex]\((8 - 3i) \cdot (8 + 8i)\)[/tex]:

1. Apply the distributive property (also known as the FOIL method):
[tex]\[ \begin{align*} (8 - 3i)(8 + 8i) &= 8 \cdot 8 + 8 \cdot 8i - 3i \cdot 8 - 3i \cdot 8i \\ &= 64 + 64i - 24i - 24i^2 \end{align*} \][/tex]

2. Simplify the expression by combining like terms and remembering that [tex]\(i^2 = -1\)[/tex]:
[tex]\[ \begin{align*} 64 + 64i - 24i - 24(-1) &= 64 + 40i + 24 \\ &= 88 + 40i \end{align*} \][/tex]

Now, subtract this product from the original complex number [tex]\((8 - 3i)\)[/tex]:
[tex]\[ (8 - 3i) - (88 + 40i) \][/tex]

3. Distribute the negative sign:
[tex]\[ \begin{align*} (8 - 3i) - (88 + 40i) &= 8 - 3i - 88 - 40i \\ &= 8 - 88 - 3i - 40i \\ &= -80 - 43i \end{align*} \][/tex]

Therefore, the value of the expression [tex]\((8 - 3i) - (8 - 3i)(8 + 8i)\)[/tex] is:
[tex]\[ \boxed{-80 - 43i} \][/tex]

Thus, the correct answer is:
A. [tex]\(-80 - 43i\)[/tex]
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