Find the real values of x and y for which:

x + 4yi = ix + y + 3

Given: x + 4yi = ix + y + 3

or x + 4yi = ix + (y + 3)

Comparing the real parts, we get

x = y + 3

or x – y = 3 …(i)

Comparing the imaginary parts, we get

4y = x …(ii)

Putting the value of x = 4y in eq. (i), we get

4y – y = 3

⇒ 3y = 3

⇒ y = 1

Putting the value of y = 1 in eq. (ii), we get

x = 4(1) = 4

Hence, the value of x = 4 and y = 1