Answered

Uncover valuable information and solutions with IDNLearn.com's extensive Q&A platform. Discover in-depth answers to your questions from our community of experienced professionals.

Simplify the expression below as much as possible.

[tex]\[ (8 + 5i) + (10 + 6i) - (3 + 6i) \][/tex]

A. [tex]\(15 + 5i\)[/tex]

B. [tex]\(21 + 5i\)[/tex]

C. [tex]\(15 + 17i\)[/tex]

D. [tex]\(21 + 17i\)[/tex]

Sagot :

GinnyAnsweridn
To simplify the expression [tex]\((8 + 5i) + (10 + 6i) - (3 + 6i)\)[/tex], we can follow these step-by-step instructions:

1. Combine the real parts of the complex numbers:
- The real parts of the complex numbers are [tex]\(8\)[/tex], [tex]\(10\)[/tex], and [tex]\(3\)[/tex].
- Add and subtract the real parts:
[tex]\[ 8 + 10 - 3 = 15 \][/tex]

2. Combine the imaginary parts of the complex numbers:
- The imaginary parts of the complex numbers are [tex]\(5i\)[/tex], [tex]\(6i\)[/tex], and [tex]\(6i\)[/tex].
- Add and subtract the imaginary parts:
[tex]\[ 5i + 6i - 6i = 5i \][/tex]

3. Combine the results from the real and imaginary parts:
- After combining, we get:
[tex]\[ 15 + 5i \][/tex]

Thus, the simplified expression is [tex]\(15 + 5i\)[/tex].

The correct answer is:
[tex]\[ \boxed{A. \; 15 + 5i} \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.