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What is the additive inverse of the complex number [tex]-12 + 4i[/tex]?

A. [tex]-12 - 4i[/tex]
B. [tex]-12 + 4i[/tex]
C. [tex]12 - 4i[/tex]
D. [tex]12 + 4i[/tex]

Sagot :

GinnyAnswer
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]
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