To simplify \( i^4 \):

1. Recall that \( i \) is the imaginary unit, defined as \( i = \sqrt{-1} \).
2. Powers of \( i \) cycle in a specific pattern:
   - \( i^1 = i \)
   - \( i^2 = -1 \)
   - \( i^3 = -i \)
   - \( i^4 = 1 \)

So, \( i^4 = 1 \).

**Answer:** \( i^4 = 1 \)

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. What is the value of \( i^5 \)?
2. How do higher powers of \( i \) continue the pattern?
3. What are the applications of imaginary numbers in mathematics?
4. How can complex numbers be represented on a plane?
5. How does one simplify \( i^{10} \)?

**Tip:** When dealing with powers of \( i \), remember the four-term cycle: \( i, -1, -i, 1 \).

Learn how to simplify i^4, using the cycle of powers of the imaginary unit i. This solution demonstrates the pattern of powers of i and explains how i^4 simplifies to 1. Perfect for high school students studying complex numbers.

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