To solve for the sum of the complex numbers [tex]\(12 - 5i\)[/tex] and [tex]\(-3 + 4i\)[/tex], we can follow these steps:
1. Identify the Real and Imaginary Parts:
- The first complex number is [tex]\(12 - 5i\)[/tex]. Here, the real part is 12 and the imaginary part is -5.
- The second complex number is [tex]\(-3 + 4i\)[/tex]. Here, the real part is -3 and the imaginary part is 4.
2. Add the Real Parts Together:
- [tex]\(12 + (-3) = 12 - 3 = 9\)[/tex].
3. Add the Imaginary Parts Together:
- [tex]\(-5i + 4i = (-5 + 4)i = -1i = -i\)[/tex].
4. Combine the Results:
- The sum of the two complex numbers is [tex]\(9 - i\)[/tex].
Given the options:
1. [tex]\(-16 + 63i\)[/tex]
2. [tex]\(9 - i\)[/tex]
3. [tex]\(9 - 9i\)[/tex]
4. [tex]\(15 - 9i\)[/tex]
We see that the correct choice is [tex]\(9 - i\)[/tex].
Therefore, the sum of [tex]\(12 - 5i\)[/tex] and [tex]\(-3 + 4i\)[/tex] is [tex]\(\boxed{9 - i}\)[/tex], which corresponds to option 2.
