To simplify the expression [tex]\((7+10i)+(4-10i)-(7-5i)\)[/tex], follow these steps:
1. Group the real and imaginary parts separately:
- Real parts: [tex]\(7 + 4 - 7\)[/tex]
- Imaginary parts: [tex]\(10i - 10i - (-5i)\)[/tex]
2. Combine the real parts:
- Add and subtract the real numbers:
[tex]\[
7 + 4 - 7 = 4
\][/tex]
3. Combine the imaginary parts:
- Add and subtract the imaginary numbers:
[tex]\[
10i - 10i + 5i = 5i
\][/tex]
4. Combine the results to form the simplified expression:
- Real part [tex]\(4\)[/tex] and imaginary part [tex]\(5i\)[/tex] give us:
[tex]\[
4 + 5i
\][/tex]
Therefore, the simplified expression is [tex]\(4 + 5i\)[/tex].
The correct answer is [tex]\( \boxed{4+5i} \)[/tex], which corresponds to option C.
