Let's simplify the expression [tex]\((6-i) + (4+2i) - (-2+i)\)[/tex] step-by-step.
1. Combine Like Terms:
First, identify and group the real and imaginary parts of the complex numbers:
[tex]\[
(6 - i) + (4 + 2i) - (-2 + i)
\][/tex]
2. Distribute the Negative Sign:
When subtracting the complex number [tex]\((-2 + i)\)[/tex], distribute the negative sign across both terms within the parentheses:
[tex]\[
(6 - i) + (4 + 2i) + 2 - i
\][/tex]
3. Combine the Real Parts:
Add the real parts together. The real terms here are [tex]\(6\)[/tex], [tex]\(4\)[/tex], and [tex]\(2\)[/tex]:
[tex]\[
6 + 4 + 2 = 12
\][/tex]
4. Combine the Imaginary Parts:
Add the imaginary parts together. The imaginary terms are [tex]\(-i\)[/tex], [tex]\(2i\)[/tex], and [tex]\(-i\)[/tex]:
[tex]\[
-i + 2i - i = 0
\][/tex]
5. Construct the Simplified Expression:
Now combine the simplified real and imaginary parts to form the final simplified expression:
[tex]\[
12 + 0i = 12
\][/tex]
So, the final result is simply [tex]\(12\)[/tex].
The correct answer is:
B. 12
