We are asked to evaluate the expression $(2 + \sqrt{-4})(-1 + \sqrt{-9})$. This involves complex numbers.

1. Problem Description

We are asked to evaluate the expression $(2 + \sqrt{-4})(-1 + \sqrt{-9})$. This involves complex numbers.

2. Solution Steps

First, we simplify the square roots of negative numbers using the definition $i = \sqrt{-1}$.

$\sqrt{-4} = \sqrt{4 \cdot -1} = \sqrt{4} \cdot \sqrt{-1} = 2i$

$\sqrt{-9} = \sqrt{9 \cdot -1} = \sqrt{9} \cdot \sqrt{-1} = 3i$

Now substitute these into the expression:

$(2 + 2i)(-1 + 3i)$

Next, we multiply the two complex numbers using the distributive property (FOIL):

$(2 + 2i)(-1 + 3i) = 2(-1) + 2(3i) + 2i(-1) + 2i(3i)$

$= -2 + 6i - 2i + 6i^2$

Since $i^2 = -1$, we have:

$-2 + 6i - 2i + 6(-1) = -2 + 4i - 6 = -8 + 4i$

3. Final Answer

$-8 + 4i$