To solve the problem of finding the value of the expression [tex]\( (-10 - 2i) + (3 + i) \)[/tex], let’s follow these steps:
1. Separate the real and imaginary parts:
The first complex number is [tex]\(-10 - 2i\)[/tex], where [tex]\(-10\)[/tex] is the real part and [tex]\(-2i\)[/tex] is the imaginary part.
The second complex number is [tex]\(3 + i\)[/tex], where [tex]\(3\)[/tex] is the real part and [tex]\(i\)[/tex] is the imaginary part.
2. Add the real parts:
Combine the real parts of both the complex numbers:
[tex]\[
-10 + 3 = -7
\][/tex]
3. Add the imaginary parts:
Combine the imaginary parts of both the complex numbers:
[tex]\[
-2i + i = -i
\][/tex]
4. Form the resulting complex number:
Combine the results from the real and imaginary parts:
[tex]\[
-7 - i
\][/tex]
So the expression [tex]\((-10 - 2i) + (3 + i)\)[/tex] simplifies to [tex]\(-7 - i\)[/tex].
Therefore, the expression equal to [tex]\((-10 - 2i) + (3 + i)\)[/tex] is:
[tex]\(\boxed{-7 - i}\)[/tex]
