Answered

IDNLearn.com: Your one-stop destination for reliable answers to diverse questions. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.

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].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.