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)
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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**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.
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