Question

what is the additive inverse of the complex number -8 + 3i?
-8 - 3i
-8 + 3i
8 - 3i
8 + 3i

Explanation:

Step1: Recall Additive Inverse Definition

The additive inverse of a complex number \( z = a + bi \) is a number \( z' \) such that \( z + z' = 0 \). Mathematically, if \( z = a + bi \), then \( z' = -a - bi \) (since \( (a + bi) + (-a - bi)=0 \)).

Step2: Apply to Given Complex Number

Given the complex number \( z=-8 + 3i \), here \( a=-8 \) and \( b = 3 \). Using the formula for the additive inverse \( z'=-a - bi \), we substitute \( a=-8 \) and \( b = 3 \):

• First, find \( -a \): \( -a=-(-8)=8 \)
• Then, find \( -bi \): \( -bi=-3i \)

So the additive inverse of \( -8 + 3i \) is \( 8-3i \).

Answer:

\( 8 - 3i \) (corresponding to the option "8 - 3i")