To evaluate the given expression:

$(-i)^{10} - \sqrt{36}$

We can break this down into two parts: $(-i)^{10}$ and $\sqrt{36}$.

Step 1: Evaluate $(-i)^{10}$

The imaginary unit $i$ is defined as $i = \sqrt{-1}$, and powers of $i$ cycle in a repeating pattern every 4 terms:

$i^1 = i, \quad i^2 = -1, \quad i^3 = -i, \quad i^4 = 1$

Now, let's evaluate $(-i)^{10}$. We can express this as $(-i)^2$ raised to the power of 5:

$(-i)^{10} = \left( (-i)^2 \right)^5 = (-1)^5 = -1$

Step 2: Evaluate $\sqrt{36}$

The square root of 36 is:

$\sqrt{36} = 6$

Step 3: Subtract the results

Now, subtract the results from Step 1 and Step 2:

$(-i)^{10} - \sqrt{36} = -1 - 6 = -7$

Thus, the value of the expression is:

$\boxed{-7}$

Would you like more details or further clarification?

---

Here are 5 related questions to consider:

1. What is the general formula for powers of $i$?
2. How do you simplify powers of negative imaginary numbers like $(-i)$?
3. Can you evaluate $(-i)^{15}$ using a similar approach?
4. How do complex numbers relate to Euler's formula?
5. What are the square roots of negative numbers in terms of $i$?

Tip: When working with powers of $i$, remember the cyclical nature of the powers: $i, -1, -i, 1$. This can help simplify complex expressions.