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,...
Related questions
Question
![**Problem 11: Find \( m \) and \( n \).**
**a.**
\[ 35 - 28i = 5m + 4ni \]
**b.**
\[ (6 - m) + 3ni = -12 + 27i \]
### Explanation
For each part, solve for the variables \( m \) and \( n \) by equating the real and imaginary components of the complex numbers.
#### Part a:
- Real part equation: \( 35 = 5m \)
- Imaginary part equation: \( -28 = 4n \)
#### Part b:
- Real part equation: \( 6 - m = -12 \)
- Imaginary part equation: \( 3n = 27 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffac1bf48-50df-4cbd-860a-5a4ad873c531%2F6566cb33-f871-477d-a176-64bd67a75203%2Fs72yji5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 11: Find \( m \) and \( n \).**
**a.**
\[ 35 - 28i = 5m + 4ni \]
**b.**
\[ (6 - m) + 3ni = -12 + 27i \]
### Explanation
For each part, solve for the variables \( m \) and \( n \) by equating the real and imaginary components of the complex numbers.
#### Part a:
- Real part equation: \( 35 = 5m \)
- Imaginary part equation: \( -28 = 4n \)
#### Part b:
- Real part equation: \( 6 - m = -12 \)
- Imaginary part equation: \( 3n = 27 \)
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