To solve the expression \((3.4+\sqrt{-25}) - (-9-\sqrt{-9})\), we will first simplify the square root terms.
-
Evaluate \(\sqrt{-25}\): \[ \sqrt{-25} = \sqrt{25} \cdot i = 5i \]
-
Evaluate \(\sqrt{-9}\): \[ \sqrt{-9} = \sqrt{9} \cdot i = 3i \]
Now, substitute these results back into the expression:
\[ (3.4 + 5i) - (-9 - 3i) \]
This simplifies to:
\[ (3.4 + 5i) + (9 + 3i) \]
Now, combine the real and imaginary parts:
-
Real part: \[ 3.4 + 9 = 12.4 \]
-
Imaginary part: \[ 5i + 3i = 8i \]
So the expression simplifies to:
\[ 12.4 + 8i \]
Thus, the final answer in the form \(a + bi\) is:
\[ \boxed{12.4 + 8i} \]