To determine the additive inverse of the complex number [tex]\(-8 + 3i\)[/tex], follow these steps:
1. Understand what the additive inverse means: The additive inverse of a number is another number that, when added to the original number, results in zero. For a complex number [tex]\( a + bi \)[/tex], its additive inverse will be [tex]\( -a - bi \)[/tex] because:
[tex]\[
(a + bi) + (-a - bi) = a + bi - a - bi = 0
\][/tex]
2. Identify the real and imaginary components: In the given complex number [tex]\(-8 + 3i\)[/tex]:
- The real part is [tex]\(-8\)[/tex].
- The imaginary part is [tex]\(3i\)[/tex].
3. Find the additive inverse for each part:
- The additive inverse of the real part [tex]\(-8\)[/tex] is [tex]\(8\)[/tex] ([tex]\(-(-8) = 8\)[/tex]).
- The additive inverse of the imaginary part [tex]\(3i\)[/tex] is [tex]\(-3i\)[/tex] ([tex]\(-3i\)[/tex]).
4. Combine these parts to form the additive inverse of the complex number:
[tex]\[
8 - 3i
\][/tex]
Therefore, the additive inverse of the complex number [tex]\(-8 + 3i\)[/tex] is [tex]\[\boxed{8 - 3i}\][/tex].
