Powers of 'i' Worksheet
Explore the cyclical nature of powers of the imaginary unit 'i' and simplify complex expressions.
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Powers of 'i' Worksheet
Name:
Date:
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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.
1
-1
i
-i
5. Which of the following is equivalent to i⁴²?
1
-1
i
-i
6. Simplify i⁷⁵. Explain your steps.
7. Simplify i¹⁰⁰.
8. i³² = 1
True
False
9. i⁵⁰ = i
True
False
10. Explain why the powers of 'i' follow a cyclical pattern. What is the significance of this cycle when simplifying expressions?
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