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].
