To subtract the complex numbers [tex]\((-8 + 4i)\)[/tex] and [tex]\((8 + 10i)\)[/tex], we need to subtract both the real and imaginary parts separately.
Step 1: Subtract the real parts.
The real part of [tex]\((-8 + 4i)\)[/tex] is [tex]\(-8\)[/tex] and the real part of [tex]\((8 + 10i)\)[/tex] is [tex]\(8\)[/tex].
Subtract the real parts:
[tex]\[
-8 - 8 = -16
\][/tex]
Step 2: Subtract the imaginary parts.
The imaginary part of [tex]\((-8 + 4i)\)[/tex] is [tex]\(4i\)[/tex] and the imaginary part of [tex]\((8 + 10i)\)[/tex] is [tex]\(10i\)[/tex].
Subtract the imaginary parts:
[tex]\[
4i - 10i = -6i
\][/tex]
Step 3: Combine the results.
Combine the results from Step 1 and Step 2 to arrive at the complex number:
[tex]\[
-16 - 6i
\][/tex]
Therefore, the result of subtracting the complex numbers [tex]\((-8 + 4i)\)[/tex] and [tex]\((8 + 10i)\)[/tex] is:
[tex]\[
\boxed{-16 - 6i}
\][/tex]
