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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Question
![**Problem:**
Find the values of \( x \) and \( y \) that make the equation true.
\[ 3x + 8i = 12 - (12y)i \]
**Explanation:**
This equation involves complex numbers, where \( i \) is the imaginary unit. The goal is to find the values of \( x \) and \( y \) such that the real parts and the imaginary parts on both sides of the equation are equal.
- **Step 1: Equate the real parts**
The real part on the left side is \( 3x \), and the real part on the right side is \( 12 \). Therefore:
\[ 3x = 12 \]
- **Step 2: Equate the imaginary parts**
The imaginary part on the left side is \( 8i \), and the imaginary part on the right side is \( -(12y)i \). Therefore:
\[ 8 = -12y \]
By solving these two equations, you can find the values of \( x \) and \( y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf296cec-535a-4e9a-8e39-6d2aa448d17e%2Fb9140f4a-f2ac-4afd-bfae-ed8b3f3eeb63%2Fcva6cwc_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find the values of \( x \) and \( y \) that make the equation true.
\[ 3x + 8i = 12 - (12y)i \]
**Explanation:**
This equation involves complex numbers, where \( i \) is the imaginary unit. The goal is to find the values of \( x \) and \( y \) such that the real parts and the imaginary parts on both sides of the equation are equal.
- **Step 1: Equate the real parts**
The real part on the left side is \( 3x \), and the real part on the right side is \( 12 \). Therefore:
\[ 3x = 12 \]
- **Step 2: Equate the imaginary parts**
The imaginary part on the left side is \( 8i \), and the imaginary part on the right side is \( -(12y)i \). Therefore:
\[ 8 = -12y \]
By solving these two equations, you can find the values of \( x \) and \( y \).
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