Solve each of the following equations for real x and y :
`(x+yi) - (7+4i) =3- 5i`

Answer

To solve the equation \((x + yi) - (7 + 4i) = 3 - 5i\) for real \(x\) and \(y\), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ (x + yi) - (7 + 4i) = 3 - 5i \]
We can rewrite this as:
\[ x + yi - 7 - 4i = 3 - 5i \]

### Step 2: Combine like terms
Now, we can rearrange the equation to group the real and imaginary parts:
\[ (x - 7) + (y - 4)i = 3 - 5i \]

### Step 3: Compare real and imaginary parts
Next, we compare the real parts and the imaginary parts on both sides of the equation:
- Real part: \(x - 7 = 3\)
- Imaginary part: \(y - 4 = -5\)

### Step 4: Solve for \(x\)
From the real part equation:
\[ x - 7 = 3 \]
Adding 7 to both sides gives:
\[ x = 3 + 7 = 10 \]

### Step 5: Solve for \(y\)
From the imaginary part equation:
\[ y - 4 = -5 \]
Adding 4 to both sides gives:
\[ y = -5 + 4 = -1 \]

### Final Solution
Thus, the solution to the equation is:
\[ x = 10 \quad \text{and} \quad y = -1 \]