Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
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]
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]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.