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Simplify the expression below as much as possible.

[tex]\[ (6 - i) + (4 + 2i) - (-2 + i) \][/tex]

A. 8
B. 12
C. [tex]\[ 12 + 2i \][/tex]
D. [tex]\[ 8 + 2i \][/tex]

Sagot :

GinnyAnsweridn
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
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