To compute $(-i)^4$:

1. Simplify the base: Recall that $i$ represents the imaginary unit, where $i^2 = -1$. So, $-i$ is simply the negative of $i$.

2. Use exponent rules: The expression can be written as: $(-i)^4 = ((-i)^2)^2$

3. Simplify $(-i)^2$: $(-i)^2 = (-i) \cdot (-i) = (-1)^2 \cdot i^2 = 1 \cdot (-1) = -1$

4. Raise to the second power: $((-i)^2)^2 = (-1)^2 = 1$

Thus, $(-i)^4 = 1$.

---

Would you like more details or have any questions?
Here are 5 related questions to expand your understanding:

1. What is $i^3$ and how can we compute it?
2. How does the cycle of powers of $i$ work (e.g., $i^1, i^2, i^3, i^4$)?
3. What is $(-i)^6$?
4. How can we represent $(-i)$ in polar form and compute its powers?
5. What happens when you compute $(-i)^{10}$?

Tip: Remember that powers of $i$ follow a repeating cycle every 4 steps: $i, -1, -i, 1$.