To determine the additive inverse of the complex number [tex]\(9 - 4i\)[/tex], follow these steps:
1. Understand the concept of an additive inverse:
- The additive inverse of a number is what you add to the original number to get zero. For any complex number [tex]\(a + bi\)[/tex], its additive inverse is [tex]\(-a - bi\)[/tex].
2. Identify the parts of the given complex number [tex]\(9 - 4i\)[/tex]:
- Here, the real part ([tex]\(a\)[/tex]) is 9.
- The imaginary part ([tex]\(b\)[/tex]) is -4 (-4i).
3. Apply the concept of additive inverse to each part:
- The additive inverse of the real part [tex]\(9\)[/tex] is [tex]\(-9\)[/tex].
- The additive inverse of the imaginary part [tex]\(-4i\)[/tex] is [tex]\(+4i\)[/tex].
4. Combine the results:
- Thus, the additive inverse of [tex]\(9 - 4i\)[/tex] is [tex]\(-9 + 4i\)[/tex].
Therefore, the additive inverse of the complex number [tex]\(9 - 4i\)[/tex] is [tex]\(-9 + 4i\)[/tex].
From the given options:
- [tex]\(-9 - 4i\)[/tex]
- [tex]\(-9 + 4i\)[/tex]
- [tex]\(9 - 4i\)[/tex]
- [tex]\(9 + 4i\)[/tex]
The correct answer is [tex]\(-9 + 4i\)[/tex].
