Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Practice Question
#### Topics: Mathematical Analysis, Complex Numbers
**Question:** Simplify the following expression:
\[ (5 + 6i) - (8 - 3i) \]
**Options:**
- \( \quad \) \(-3 + 9i\)
- \( \quad \) \(6i\)
- \( \quad \) \(-9 + 3i\)
- \( \quad \) \(-6i\)
### Explanation:
To simplify the expression \((5 + 6i) - (8 - 3i)\), follow these steps:
1. **Distribute the negative sign:**
\[
(5 + 6i) - 8 + 3i
\]
Which simplifies to:
\[
5 + 6i - 8 + 3i
\]
2. **Combine like terms:**
- Combine the real parts: \(5 - 8 = -3\)
- Combine the imaginary parts: \(6i + 3i = 9i\)
Therefore, the simplified expression is:
\[
-3 + 9i
\]
### Correct Answer:
\(-3 + 9i\)
### Graphs/Diagrams:
There are no graphs or diagrams in this problem. The question is purely algebraic, involving the arithmetic of complex numbers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa94e8ccf-9a33-47ca-bbab-b929f0edf049%2F7ce11084-3a9d-4847-b204-0f454fd10304%2F87kf3bq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Practice Question
#### Topics: Mathematical Analysis, Complex Numbers
**Question:** Simplify the following expression:
\[ (5 + 6i) - (8 - 3i) \]
**Options:**
- \( \quad \) \(-3 + 9i\)
- \( \quad \) \(6i\)
- \( \quad \) \(-9 + 3i\)
- \( \quad \) \(-6i\)
### Explanation:
To simplify the expression \((5 + 6i) - (8 - 3i)\), follow these steps:
1. **Distribute the negative sign:**
\[
(5 + 6i) - 8 + 3i
\]
Which simplifies to:
\[
5 + 6i - 8 + 3i
\]
2. **Combine like terms:**
- Combine the real parts: \(5 - 8 = -3\)
- Combine the imaginary parts: \(6i + 3i = 9i\)
Therefore, the simplified expression is:
\[
-3 + 9i
\]
### Correct Answer:
\(-3 + 9i\)
### Graphs/Diagrams:
There are no graphs or diagrams in this problem. The question is purely algebraic, involving the arithmetic of complex numbers.
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