We are given the equation:

$(x + yi) + (4 + 9i) = 9 - 4i$

To solve for $x$ and $y$, we will equate both the real and imaginary parts on the left-hand side and right-hand side.

1. First, simplify the left-hand side: $(x + yi) + (4 + 9i) = (x + 4) + (y + 9)i$

Now the equation becomes: $(x + 4) + (y + 9)i = 9 - 4i$

2. Equate the real parts and the imaginary parts:

   • Real part: $x + 4 = 9$
   • Imaginary part: $y + 9 = -4$

3. Solve for $x$ and $y$:

   • $x + 4 = 9 \Rightarrow x = 5$
   • $y + 9 = -4 \Rightarrow y = -13$

Therefore, the solution is $x = 5$ and $y = -13$.

The correct answer is A.

Would you like further explanation or have any questions?

Here are 5 related questions:

1. How do you solve equations with complex numbers?
2. Why do we equate the real and imaginary parts separately?
3. What is the role of $i$ in complex numbers?
4. Can complex numbers be graphed on a plane?
5. How do complex numbers apply in physics and engineering?

Tip: Always remember to separate real and imaginary parts when solving equations with complex numbers.