Let's evaluate the expression step by step.
We start with the expression:
\[ (13 + \sqrt{-225}) - (\sqrt{49} - 2i) \]
First, simplify \(\sqrt{-225}\): \[ \sqrt{-225} = \sqrt{225} \cdot \sqrt{-1} = 15i \]
Now the expression becomes: \[ (13 + 15i) - (\sqrt{49} - 2i) \]
Next, simplify \(\sqrt{49}\): \[ \sqrt{49} = 7 \]
Now substituting this back into the expression gives: \[ (13 + 15i) - (7 - 2i) \]
Distributing the negative sign: \[ 13 + 15i - 7 + 2i \]
Now combine the real parts and the imaginary parts: \[ (13 - 7) + (15i + 2i) = 6 + 17i \]
Thus, the final result in the form \(a + bi\) is: \[ \boxed{6 + 17i} \]