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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.

(x + yi) + (4 + 9i) = 9 - 4i. What are the values of x and y?

Learn how to solve the complex number equation (x + yi) + (4 + 9i) = 9 - 4i by equating the real and imaginary parts. The problem explores basic concepts in complex numbers, including simplifying and solving for x and y.

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