To subtract the complex number [tex]\(8 + 7i\)[/tex] from [tex]\(4 - 16i\)[/tex], follow these steps:
1. Write down the complex numbers:
- The first complex number is [tex]\(4 - 16i\)[/tex].
- The second complex number is [tex]\(8 + 7i\)[/tex].
2. Set up the subtraction:
[tex]\[
(4 - 16i) - (8 + 7i)
\][/tex]
3. Distribute the subtraction across the real and imaginary parts:
[tex]\[
(4 - 8) + (-16i - 7i)
\][/tex]
4. Perform the subtraction on the real parts:
[tex]\[
4 - 8 = -4
\][/tex]
5. Perform the subtraction on the imaginary parts:
[tex]\[
-16i - 7i = -23i
\][/tex]
6. Combine the results:
[tex]\[
-4 - 23i
\][/tex]
So, the result of subtracting [tex]\(8 + 7i\)[/tex] from [tex]\(4 - 16i\)[/tex] is [tex]\(-4 - 23i\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{-4 - 23i} \][/tex]
Thus, the correct choice is D. [tex]$-4 - 23 i$[/tex].
