1. The problem asks to simplify $$(-2 + \sqrt{-4}) + (3 - \sqrt{-7})$$ in the form $$a + bi$$ where $$a$$ and $$b$$ are real numbers. 2. Recall that $$\sqrt{-1} = i$$, the imaginary unit. 3. We can write $$\sqrt{-4} = \sqrt{4 \cdot (-1)} = \sqrt{4} \cdot \sqrt{-1} = 2i$$. 4. Similarly, $$\sqrt{-7} = \sqrt{7 \cdot (-1)} = \sqrt{7} \cdot i = \sqrt{7}i$$. 5. Substitute these back into the expression: $$(-2 + 2i) + (3 - \sqrt{7}i)$$ 6. Group the real parts and imaginary parts: Real: $$-2 + 3 = 1$$ Imaginary: $$2i - \sqrt{7}i = (2 - \sqrt{7})i$$ 7. Therefore, the expression simplifies to: $$1 + (2 - \sqrt{7})i$$ 8. The final answer in the form $$a + bi$$ is: $$\boxed{1 + (2 - \sqrt{7})i}$$