Powers of 'i' Worksheet
Explore the cyclical nature of powers of the imaginary unit 'i' and simplify complex expressions.
Includes
Fill in the BlanksMultiple ChoiceShort AnswerTrue / False
Standards
CCSS.MATH.CONTENT.HSN.CN.A.1CCSS.MATH.CONTENT.HSN.CN.A.2
Topics
mathalgebracomplex numberspowers of iimaginary numbers
6 sections · Free to use · Printable
Powers of 'i' Worksheet
Name:
Date:
Score:
Read each question carefully and provide the correct answer. Remember the cyclical pattern of powers of 'i' (i, -1, -i, 1).
1. The imaginary unit 'i' is defined as the square root of .
2. The value of i¹ is .
3. The value of i² is .
4. The value of i³ is .
5. The value of i⁴ is .
6. The powers of 'i' repeat in a cycle of .
7. What is the value of i⁵?
a
1
b
i
c
-1
d
-i
8. Simplify i²³.
a
i
b
-1
c
-i
d
1
9. Explain how to find the value of i raised to any positive integer power.
10. Simplify i⁴².
11. Simplify i⁻¹⁰.
12. i¹⁰⁰ = 1
T
True
F
False
13. i³⁵ = -i
T
True
F
False