To find the additive inverse of a complex number, we need to negate both the real part and the imaginary part of the complex number.
Given the complex number [tex]\(9 - 4i\)[/tex]:
1. The real part of the number is [tex]\(9\)[/tex].
2. The imaginary part of the number is [tex]\(-4i\)[/tex].
To find the additive inverse, we negate both parts:
1. Negating the real part: [tex]\(-9\)[/tex].
2. Negating the imaginary part: [tex]\(+4i\)[/tex].
Therefore, the additive inverse of the complex number [tex]\(9 - 4i\)[/tex] is [tex]\(-9 + 4i\)[/tex].
So the correct answer is:
[tex]\[ -9 + 4i \][/tex]
