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 / FalseLong Answer
Standards
CCSS.MATH.CONTENT.HSN.CN.A.2
Topics
MathAlgebraComplex NumbersImaginary UnitPowers of i
7 sections · Free to use · Printable
Powers of 'i' Worksheet
Name:
Date:
Score:
Read each question carefully and provide the best answer. Show all your work for full credit.
1. The imaginary unit 'i' is defined as the square root of .
2. Complete the cycle of powers of 'i': i¹ = i i² = i³ = i⁴ =
3. The powers of 'i' repeat in a cycle of .
4. Simplify i¹⁹.
a
1
b
-1
c
i
d
-i
5. Which of the following is equivalent to i⁴²?
a
1
b
-1
c
i
d
-i
6. Simplify i⁷⁵. Explain your steps.
7. Simplify i¹⁰⁰.
8. i³² = 1
T
True
F
False
9. i⁵⁰ = i
T
True
F
False
10. Explain why the powers of 'i' follow a cyclical pattern. What is the significance of this cycle when simplifying expressions?