Solve each of the following equations for real x and y :
`x+2yi= i - (-3 + 5)`

Answer

To solve the equation \( x + 2yi = i - (-3 + 5) \), we will follow these steps:

### Step 1: Simplify the Right Side of the Equation
First, we simplify the right side of the equation:

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

So, the equation becomes:

\[ x + 2yi = 2 + i \]

### Step 2: Compare Real and Imaginary Parts
Now, we can compare the real and imaginary parts of both sides of the equation.

The left side is \( x + 2yi \) and the right side is \( 2 + i \).

From this, we can set up the following equations:

1. Real part: \( x = 2 \)
2. Imaginary part: \( 2y = 1 \)

### Step 3: Solve for \( x \)
From the first equation, we have:

\[ x = 2 \]

### Step 4: Solve for \( y \)
From the second equation, we can solve for \( y \):

\[ 2y = 1 \implies y = \frac{1}{2} \]

### Final Solution
Thus, the solution for the values of \( x \) and \( y \) is:

\[ x = 2, \quad y = \frac{1}{2} \]

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