Let's solve the given expression step-by-step to find out which complex number is equivalent to it:
Given expression:
[tex]\[ 7 + (9 + 27i) - 2(25 - 11i) \][/tex]
### Step 1: Distribute the [tex]\(-2\)[/tex] across the terms inside the parentheses
[tex]\[
-2(25 - 11i) = -2 \cdot 25 + -2 \cdot -11i = -50 + 22i
\][/tex]
### Step 2: Substitute this result back into the original expression
[tex]\[
7 + (9 + 27i) - 50 + 22i
\][/tex]
### Step 3: Combine the real parts and the imaginary parts separately
- Real parts: [tex]\(7 + 9 - 50\)[/tex]
[tex]\[
7 + 9 = 16
\][/tex]
[tex]\[
16 - 50 = -34
\][/tex]
- Imaginary parts: [tex]\(27i + 22i\)[/tex]
[tex]\[
27i + 22i = 49i
\][/tex]
### Final result in complex form
[tex]\[
-34 + 49i
\][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{-34 + 49i} \][/tex]
So, the correct answer is D. [tex]\(-34 + 49i\)[/tex].
