find x and y

x+5i=y-yi

To find the values of x and y in the equation x + 5i = y - yi, we can equate the real and imaginary parts of both sides of the equation separately.

The real parts are x and y, and the imaginary parts are 5i and -yi.

Equating the real parts, we have:
x = y

Equating the imaginary parts, we have:
5i = -yi

To solve this, we'll isolate the variable y.

Divide both sides of the equation by i:
(5i) / i = (-yi) / i

This simplifies to:
5 = -y

Now, multiply both sides of the equation by -1 to isolate y:
-1 * 5 = -1 * (-y)
-5 = y

Therefore, we have found the values of x and y:
x = y = -5.