To simplify the expression [tex]\((2 - 5i) - (4 - 4i)\)[/tex], follow these steps:
1. Distribute the subtraction across the complex numbers:
[tex]\[
(2 - 5i) - (4 - 4i) = 2 - 5i - 4 + 4i
\][/tex]
2. Combine the real parts:
[tex]\[
2 - 4 = -2
\][/tex]
3. Combine the imaginary parts:
[tex]\[
-5i + 4i = -i
\][/tex]
Putting it all together:
[tex]\[
(2 - 5i) - (4 - 4i) = -2 - i
\][/tex]
Therefore, the simplified expression is [tex]\( \boxed{-2 - i} \)[/tex].
Given the provided options:
- [tex]\(2 + i\)[/tex]
- [tex]\(-3i\)[/tex]
- [tex]\(-2 - i\)[/tex]
- [tex]\(6 - 9i\)[/tex]
The correct choice is:
[tex]\(
\boxed{-2 - i}
\)[/tex]
