Seakeeping computations in frecuency domain

beginner

I'm working in the implementation of a cfd code in order to predict the behaviour of a ship advancing in waves. In frecuency domain, i have a potential function (i'm working with a potential flow for the solution of the laplace equation) with an imaginary part. In addition, the boundary conditions include products in the form of products of i*(gradient of a complex amplitude), for example. I don't understand this. What must i do?. Work only with the real part of all the expressions?, change cos by sin?, I dont know. Where can i find numerical schemes? I'm working with the approximations explained in the final part of the book "practical ship hydrodynamics", by bertram, v. So, how can i implement the boundary condition explained in this book? (an imaginary part and a real part together?).

Thank you very much in advance