a system of curvilinear coordinates is usually expressed by an admissible transformation represented by a set of

*real scalar*functions [itex]x_i=x_i(u_1,\ldots,u_n)[/itex].

Does it make sense to form a system of curvilinear coordinates where the [itex]x_i[/tex] and [itex]u_i[/tex] functions are

*complex*valued?

If that exists, I cannot find any source in the net.