To find the sum of [tex]\( u \)[/tex] and [tex]\( v \)[/tex], where [tex]\( u = 1 + i \)[/tex] and [tex]\( v = 1 - i \)[/tex], we can perform the addition as follows:
1. First, write down the expressions for [tex]\( u \)[/tex] and [tex]\( v \)[/tex]:
[tex]\[
u = 1 + i
\][/tex]
[tex]\[
v = 1 - i
\][/tex]
2. Now, let's add [tex]\( u \)[/tex] and [tex]\( v \)[/tex]:
[tex]\[
u + v = (1 + i) + (1 - i)
\][/tex]
3. Combine the like terms (real parts and imaginary parts separately):
[tex]\[
u + v = (1 + 1) + (i - i)
\][/tex]
4. Simplify the expression:
[tex]\[
u + v = 2 + 0i
\][/tex]
[tex]\[
u + v = 2
\][/tex]
Therefore, the result of [tex]\( u + v \)[/tex] is [tex]\(\boxed{2.0}\)[/tex].
So, the correct answer is:
A. 2
