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What is the additive inverse of the complex number [tex][tex]$9-4i$[/tex][/tex]?

A. [tex][tex]$-9-4i$[/tex][/tex]

B. [tex][tex]$-9+4i$[/tex][/tex]

C. [tex][tex]$9-4i$[/tex][/tex]

D. [tex][tex]$9+4i$[/tex][/tex]

Sagot :

GinnyAnsweridn
To determine the additive inverse of the complex number [tex]\(9 - 4i\)[/tex], follow these steps:

1. Understand the concept of an additive inverse:
- The additive inverse of a number is what you add to the original number to get zero. For any complex number [tex]\(a + bi\)[/tex], its additive inverse is [tex]\(-a - bi\)[/tex].

2. Identify the parts of the given complex number [tex]\(9 - 4i\)[/tex]:
- Here, the real part ([tex]\(a\)[/tex]) is 9.
- The imaginary part ([tex]\(b\)[/tex]) is -4 (-4i).

3. Apply the concept of additive inverse to each part:
- The additive inverse of the real part [tex]\(9\)[/tex] is [tex]\(-9\)[/tex].
- The additive inverse of the imaginary part [tex]\(-4i\)[/tex] is [tex]\(+4i\)[/tex].

4. Combine the results:
- Thus, the additive inverse of [tex]\(9 - 4i\)[/tex] is [tex]\(-9 + 4i\)[/tex].

Therefore, the additive inverse of the complex number [tex]\(9 - 4i\)[/tex] is [tex]\(-9 + 4i\)[/tex].

From the given options:
- [tex]\(-9 - 4i\)[/tex]
- [tex]\(-9 + 4i\)[/tex]
- [tex]\(9 - 4i\)[/tex]
- [tex]\(9 + 4i\)[/tex]

The correct answer is [tex]\(-9 + 4i\)[/tex].
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