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
![**Understanding and Correcting Errors in Dividing Complex Numbers**
**Problem Description:**
A student attempted to divide complex numbers using the expression:
\[
\frac{1 - i}{3 - i}
\]
However, they arrived at an incorrect result:
\[
\frac{3i - 1}{10}
\]
**Error Identification:**
The incorrect division is marked with an "X", indicating a mistake.
**Options for Correcting the Error:**
**A.** The student multiplied the numerator and denominator each by their own complex conjugates rather than multiplying both by the complex conjugate of the denominator.
**B.** The student should have subtracted the result of simplifying \(i^2\) from the real terms in the numerator and denominator instead of adding.
**C.** When multiplying the numerators and denominators, the student forgot the cross terms that arise from using the Distributive Property and ended up with no imaginary parts.
**D.** The student’s final answer is correct, but it should be simplified.
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---
**Navigation:**
- Current Progress: Reviewing question 2 out of 23
- Options to proceed: "Back" or "Next >"
This guidance helps students understand common errors in working with complex numbers and provides detailed choices for identifying and correcting the mistake.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ddc4189-9420-4693-a8a5-bceb27d96194%2F7e72a127-d969-477f-974c-3324d08c4a60%2Ffke5xug.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding and Correcting Errors in Dividing Complex Numbers**
**Problem Description:**
A student attempted to divide complex numbers using the expression:
\[
\frac{1 - i}{3 - i}
\]
However, they arrived at an incorrect result:
\[
\frac{3i - 1}{10}
\]
**Error Identification:**
The incorrect division is marked with an "X", indicating a mistake.
**Options for Correcting the Error:**
**A.** The student multiplied the numerator and denominator each by their own complex conjugates rather than multiplying both by the complex conjugate of the denominator.
**B.** The student should have subtracted the result of simplifying \(i^2\) from the real terms in the numerator and denominator instead of adding.
**C.** When multiplying the numerators and denominators, the student forgot the cross terms that arise from using the Distributive Property and ended up with no imaginary parts.
**D.** The student’s final answer is correct, but it should be simplified.
**Interactive Options:**
- Video
- Textbook
- Get more help
---
**Navigation:**
- Current Progress: Reviewing question 2 out of 23
- Options to proceed: "Back" or "Next >"
This guidance helps students understand common errors in working with complex numbers and provides detailed choices for identifying and correcting the mistake.

Transcribed Image Text:### Understanding Integer Powers of Negative One
Tamara says that raising the number \(-1\) to any integer power results in either \(-1\) or \(1\) as the result, since \(i^2 = -1\). Do you agree with Tamara? Explain.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **A.** Tamara is incorrect. For integer \(n\), \(i^n\) is only certain to be \(1\) or \(-1\) if \(n\) is even. If \(n\) is odd, \(i^n\) could be ___________.
- **B.** Tamara is incorrect. Any integer could be equal to \(i^n\) if \(n\) can be any integer.
- **C.** Tamara is correct. Starting with \(i^2 = -1\), \(i^n\) can be found for any \(n\) by raising \(-1\) to the power of \(2n\), which is guaranteed to be \(-1\) or \(1\).
- **D.** Tamara is correct. Checking a single value of a function is sufficient to determine trends for all input values.
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**Interface Options:**
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**Progress Tracking:**
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