What is the additive inverse of the complex number [tex]-8+3i[/tex]?

A. [tex]-8-3i[/tex]
B. [tex]-8+3i[/tex]
C. [tex]8-3i[/tex]
D. [tex]8+3i[/tex]



Answer :

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].