To simplify the expression \((9 + -4i) + (-9 - -16i)\), we can break it down and combine the real and imaginary parts.
First, rewrite the expression: \[ (9 - 4i) + (-9 + 16i) \]
Now, combine the real and imaginary parts separately:
- Real parts: \(9 + (-9) = 0\)
- Imaginary parts: \(-4i + 16i = 12i\)
Now, putting it together, we have: \[ 0 + 12i = 12i \]
This answer does not match any of the provided options (A, B, C, D).
Let's re-check the problem for any computation errors.
- \(9 + -4i = 9 - 4i\)
- \(-9 - -16i = -9 + 16i\)
Combining:
- Real part: \(9 + (-9) = 0\)
- Imaginary part: \(-4 + 16 = 12\)
Final result: \(12i\)
Since neither the result \(12i\) nor an equivalent appears in the options listed, there seems to be a discrepancy. However, based on the calculations, the result is confirmed to be \(12i\).