To simplify the expression \(\sqrt{-49} - \sqrt{-64}\), we can use the concept of imaginary numbers. Recall that \(i\) is the imaginary unit, defined as \(i = \sqrt{-1}\).
First, we simplify each square root:
\[ \sqrt{-49} = \sqrt{49} \cdot \sqrt{-1} = 7i \]
\[ \sqrt{-64} = \sqrt{64} \cdot \sqrt{-1} = 8i \]
Now, we can substitute these back into the original expression:
\[ \sqrt{-49} - \sqrt{-64} = 7i - 8i \]
Now, we combine the terms:
\[ 7i - 8i = -1i = -i \]
Thus, the simplified expression is:
\[ \boxed{-i} \]