Powers of 'i' Worksheet
Explore and simplify expressions involving powers of the imaginary unit 'i' for Grade 12 mathematics.
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Powers of 'i' Worksheet
Name:
Date:
Score:
Read each question carefully and provide the most simplified answer. Remember the cyclical nature of the powers of 'i'.
1. What is the simplified form of i^15?
1
-1
i
-i
2. Which of the following is equivalent to i^42?
1
-1
i
-i
3. The value of i^200 is .
4. i^3 + i^7 = .
5. Simplify the expression: i^25 + i^50 + i^75 + i^100.
6. Explain the pattern of powers of 'i' and how it helps in simplifying i^n for any integer n.
7. The expression i^101 is equal to i.
True
False
8. For any positive integer n, i^(4n) = 1.
True
False
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