Homework Help is Here – Start Your Trial Now!
Math
Algebra
ASSESSMENT PRACTICE 48. Select all powers of i that are real numbers. ☐A.i □ B. i² ☐ C. 1³ ☐ D.14 0 E.15 F. ¡6

ASSESSMENT PRACTICE 48. Select all powers of i that are real numbers. ☐A.i □ B. i² ☐ C. 1³ ☐ D.14 0 E.15 F. ¡6

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,...
See similar textbooks
icon
Related questions
Question
**Assessment Practice:** **Question 48:** Select all powers of \( i \) that are real numbers. - [ ] A. \( i \) - [ ] B. \( i^2 \) - [ ] C. \( i^3 \) - [ ] D. \( i^4 \) - [ ] E. \( i^5 \) - [ ] F. \( i^6 \) **Explanation:** The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). The powers of \( i \) cycle every four: - \( i^1 = i \) - \( i^2 = -1 \) - \( i^3 = -i \) - \( i^4 = 1 \) Thus, \( i^4 \) and \( i^6 \) are real numbers since \( i^6 = (i^4)(i^2) = 1(-1) = -1 \). Therefore, the correct answers are options D and F.
Transcribed Image Text:**Assessment Practice:** **Question 48:** Select all powers of \( i \) that are real numbers. - [ ] A. \( i \) - [ ] B. \( i^2 \) - [ ] C. \( i^3 \) - [ ] D. \( i^4 \) - [ ] E. \( i^5 \) - [ ] F. \( i^6 \) **Explanation:** The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). The powers of \( i \) cycle every four: - \( i^1 = i \) - \( i^2 = -1 \) - \( i^3 = -i \) - \( i^4 = 1 \) Thus, \( i^4 \) and \( i^6 \) are real numbers since \( i^6 = (i^4)(i^2) = 1(-1) = -1 \). Therefore, the correct answers are options D and F.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS