Question

For what real values of x and y are the numbers -3+i^2y and x^2+y+4i are conjugate complex

Answer 1

-3 + i^2y = -3-y
The conjugate of x^2+y + 4i is x^2+y -4i

so, we want -3-y = x^2+y - 4i
In no case is that ever true
We can have -3-y = x^2+y, but there's no way to get the -4i

I suspect a typo in the problem.