To evaluate $\sqrt{-16} + 4\sqrt{-9}$, we can express the square roots of negative numbers in terms of imaginary numbers.

1. Calculate $\sqrt{-16}$: $\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i$ where $i$ is the imaginary unit defined as $i = \sqrt{-1}$.

2. Calculate $4\sqrt{-9}$: $4\sqrt{-9} = 4 \cdot \sqrt{9} \cdot \sqrt{-1} = 4 \cdot 3i = 12i$

3. Combine the terms: $\sqrt{-16} + 4\sqrt{-9} = 4i + 12i = 16i$

The final answer is: $16i$

Would you like more details on imaginary numbers or have any further questions?

Here are five related questions for practice:

1. What is $\sqrt{-25} + \sqrt{-36}$?
2. How would you simplify $5\sqrt{-4} - 2\sqrt{-9}$?
3. Calculate $(3 + 4i) + (5 - 7i)$.
4. Simplify $(2i)(3i)$.
5. What is the result of $i^4 + i^2$?

Tip: Remember, $\sqrt{-a} = i\sqrt{a}$ for any positive real number $a$.