https://file.aiquickdraw.com/mathbot/file/172738177980274j9rtfv.jpg

The equation provided in the image is:

\[
x + yi = (3 + 2i) + (2 - i)
\]

### Step-by-step solution:
1. **Combine the complex numbers** on the right-hand side:

\[
(3 + 2i) + (2 - i) = (3 + 2) + (2i - i)
\]
\[
= 5 + i
\]

2. So, the equation becomes:
\[
x + yi = 5 + i
\]

3. **Equate the real and imaginary parts**:
   - Real part: \(x = 5\)
   - Imaginary part: \(y = 1\)

### Final answer:
\[
x = 5, \quad y = 1
\]

Would you like any further explanation or have any questions?

### Related questions:
1. How do you add and subtract complex numbers in general?
2. What is the process of equating real and imaginary parts in complex number equations?
3. Can complex numbers be graphed, and how do you represent them on a plane?
4. How do we multiply complex numbers, and what is the role of \(i^2 = -1\)?
5. What are the practical applications of complex numbers in physics and engineering?

### Tip:
Always remember that when solving for unknowns in complex number equations, equate the real and imaginary parts separately.

Find the values of x and y that satisfy the equation x + yi = (3 + 2i) + (2 - i)

Learn how to solve the complex number equation x + yi = (3 + 2i) + (2 - i) by combining the real and imaginary parts. This step-by-step guide is perfect for students in Grades 9-11.

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