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Simplify the following expression:

[tex](-8 - 4i) + (-1 - 6i) = ?[/tex]

F. -19

G. 19

H. [tex]-19i[/tex]

J. [tex]-38i[/tex]

K. [tex]-9 - 10i[/tex]

Sagot :

GinnyAnsweridn
To solve the given problem of adding two complex numbers [tex]\((-8 - 4i)\)[/tex] and [tex]\((-1 - 6i)\)[/tex], follow these steps:

1. Identify the Real Parts:
- The real part of the first complex number [tex]\((-8 - 4i)\)[/tex] is [tex]\(-8\)[/tex].
- The real part of the second complex number [tex]\((-1 - 6i)\)[/tex] is [tex]\(-1\)[/tex].

2. Identify the Imaginary Parts:
- The imaginary part of the first complex number [tex]\((-8 - 4i)\)[/tex] is [tex]\(-4i\)[/tex].
- The imaginary part of the second complex number [tex]\((-1 - 6i)\)[/tex] is [tex]\(-6i\)[/tex].

3. Add the Real Parts:
- [tex]\(-8 + (-1) = -9\)[/tex]

4. Add the Imaginary Parts:
- [tex]\(-4i + (-6i) = -10i\)[/tex]

5. Combine the Results:
- The resulting complex number from adding the real and imaginary parts is [tex]\(-9 - 10i\)[/tex].

Therefore, [tex]\((-8 - 4i) + (-1 - 6i) = -9 - 10i\)[/tex].

So, the correct answer is:
[tex]\[ \boxed{-9 - 10i} \][/tex]
This corresponds to option [tex]\( K \)[/tex].
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