To find the additive inverse of a complex number, you need to find a number that, when added to the original complex number, results in zero. For a complex number [tex]\( a + bi \)[/tex], its additive inverse is [tex]\( -a - bi \)[/tex].
Given the complex number [tex]\(-12 + 4i\)[/tex], let's determine its additive inverse step by step:
1. Identify the real and imaginary parts:
- The real part is [tex]\(-12\)[/tex].
- The imaginary part is [tex]\(4i\)[/tex].
2. Determine the additive inverse of each part:
- The additive inverse of the real part [tex]\(-12\)[/tex] is [tex]\( 12 \)[/tex].
- The additive inverse of the imaginary part [tex]\(4i\)[/tex] is [tex]\(-4i \)[/tex].
3. Combine these to form the additive inverse of the complex number:
- The additive inverse of [tex]\(-12 + 4i\)[/tex] is [tex]\(12 - 4i \)[/tex].
Therefore, the additive inverse of the complex number [tex]\(-12 + 4i\)[/tex] is [tex]\(12 - 4i\)[/tex].
So, the correct answer is:
[tex]\[
12 - 4i
\][/tex]
