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Find the values of x and y that make the equation true. За + 8i — 12 — (12у)i – (12y)i

Find the values of x and y that make the equation true. За + 8i — 12 — (12у)i – (12y)i

Algebra and Trigonometry (6th Edition)
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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**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 \( y \).
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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