Complex numbers-finding real number pairs

Hello,

I am having trouble with this question:

__"Find all possible real number pairs p, q such that 3+5i/1+pi =q+4i"__

Im sure it's easy but I think I am overlooking something. I multiplied both sides by the conjugate of 1+pi....ie.(1-pi) but I think it's wrong.

Any help would be appreciated.

Regards,

Neverquit

found 1 solution but not the other

I found the solutions 0.25, -1 after re-arranging pq = 1 to q = 1/p to get 1/p - 4p = 3 to get quadratic 4p^2+3p-1=0.

There is also apparently another solution of 4, -1 which I can’t find.

How do I find it?