Given that x and y are real numbers, find the possible values of x and y such that (x + y) + (x - y)i equals 7 + 3i.

To find the possible values of x and y such that (x + y) + (x - y)i equals 7 + 3i, we need to compare the real parts and the imaginary parts of the complex numbers on both sides of the equation.

Let's break it down:

The given equation is:

(x + y) + (x - y)i = 7 + 3i

On the left-side of the equation, (x + y) is the real part, and (x - y)i is the imaginary part. On the right-side of the equation, 7 is the real part, and 3i is the imaginary part.

For two complex numbers to be equal, their corresponding real parts must be equal and their imaginary parts must also be equal. This means:

Real part: x + y = 7 ...(1)

Imaginary part: x - y = 3 ...(2)

Now, let's solve the system of equations formed by (1) and (2).

From equation (2):

x = 3 + y

Substituting this into equation (1):

(3 + y) + y = 7 3 + 2y = 7 2y = 7 - 3 2y = 4

Now divide both sides by 2:

y = 4 / 2 y = 2

Now that we have the value for y, we can find x using equation (2):

x - y = 3 x - 2 = 3 x = 3 + 2 x = 5

So, the possible values of x and y that satisfy the equation are:

x = 5 and y = 2.