To simplify the expression \( 1024 - (1024 - 15) \):

1. First, evaluate the expression inside the parentheses:
\[
1024 - 15 = 1009
\]

2. Now substitute back into the expression:
\[
1024 - 1009
\]

3. Finally, perform the subtraction:
\[
1024 - 1009 = 15
\]

Thus, the result is \( 15 \).