-3+i²y and x²+y+4i

Since i² = -1, which is a real number, the first one is
a real number but the second one is imaginary, so it is 
impossible for them to be conjugates!

That's because -3+i²y = -3+(-1)y = -3-y which is a 
real number and therefore it has no imaginary part. 

However x²+y+4i has an imaginary part, 4i.

Therefore no possible real numbers x and y will cause

-3+i²y and x²+y+4i to be conjugate comlex numbers, for
if a complex number has an imaginary part, its conjugate
must also have an imaginary part.

Are you sure you copied the problem correctly?

Edwin