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 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?
1
i
-1
-i
8. Simplify i²³.
i
-1
-i
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
True
False
13. i³⁵ = -i
True
False
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