lProwid%3D1168028#question7 ing er Magni fier Highlight mode Q Zoom in Q Zo out Review later 7. Elizabeth tried to find the product of (2 + 4i) and (3 – i), and her work is shown below. Identify the error in the process shown and determine the correct product of (2 + 4i) and (3- i). A 面 Gi (2+4i)(3 – i) = 6-2i+12i-4;? = 6+10i – 4 = 6+10i -4(1) = 6+10i -4 = 2+10i
lProwid%3D1168028#question7 ing er Magni fier Highlight mode Q Zoom in Q Zo out Review later 7. Elizabeth tried to find the product of (2 + 4i) and (3 – i), and her work is shown below. Identify the error in the process shown and determine the correct product of (2 + 4i) and (3- i). A 面 Gi (2+4i)(3 – i) = 6-2i+12i-4;? = 6+10i – 4 = 6+10i -4(1) = 6+10i -4 = 2+10i
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 Statement
Elizabeth tried to find the product of \((2 + 4i)\) and \((3 - i)\), and her work is shown below. Identify the error in the process shown and determine the correct product of \((2 + 4i)\) and \((3 - i)\).
### Work Shown
\[
(2 + 4i)(3 - i)
\]
\[
= 6 - 2i + 12i - 4i^2
\]
\[
= 6 + 10i - 4i^2
\]
\[
= 6 + 10i - 4(1)
\]
\[
= 6 + 10i - 4
\]
\[
= 2 + 10i
\]
### Explanation
Elizabeth's error occurs in the treatment of \(i^2\). Recall that \(i^2 = -1\), not \(1\).
### Correct Calculation
Re-evaluate using the property \(i^2 = -1\):
\[
= 6 - 2i + 12i - 4i^2
\]
\[
= 6 + 10i - 4(-1)
\]
\[
= 6 + 10i + 4
\]
\[
= 10 + 10i
\]
Thus, the correct product is \(10 + 10i\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc82ecbe8-fc89-4ada-9c8e-54bf4ff00369%2Fb0e08200-8ac8-4e5b-8a5a-53a136905466%2Fhoq2o9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Elizabeth tried to find the product of \((2 + 4i)\) and \((3 - i)\), and her work is shown below. Identify the error in the process shown and determine the correct product of \((2 + 4i)\) and \((3 - i)\).
### Work Shown
\[
(2 + 4i)(3 - i)
\]
\[
= 6 - 2i + 12i - 4i^2
\]
\[
= 6 + 10i - 4i^2
\]
\[
= 6 + 10i - 4(1)
\]
\[
= 6 + 10i - 4
\]
\[
= 2 + 10i
\]
### Explanation
Elizabeth's error occurs in the treatment of \(i^2\). Recall that \(i^2 = -1\), not \(1\).
### Correct Calculation
Re-evaluate using the property \(i^2 = -1\):
\[
= 6 - 2i + 12i - 4i^2
\]
\[
= 6 + 10i - 4(-1)
\]
\[
= 6 + 10i + 4
\]
\[
= 10 + 10i
\]
Thus, the correct product is \(10 + 10i\).
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