Apparently, the built-in App (Solve) doesn't allow complex starting values, and doesn't search for complex solutions - - or does it?

I tried to use csolve(), but that only allows a single equation to be entered, and also fsolve(), but the syntax is not clear to me. The help screen states, that a numerical solution of a system of equations can be returned, but the syntax given is fsolve(Expr, Var, [Guess or interval], [Method]). I'm not sure how to use this with more than one non-linear equation.

By the way, how many methods are there to choose from? Not clear from the user's guide).

I'm really looking for something like Sune Bredahl's excellent Solvesys for the HP49G+ and HP50G (couldn't something along those lines have been implemented for the Prime?), or even like the somewhat clunkier and slower MSLV (both return complex solutions).

For the built in solver (numeric view), some diagnostic output would be helpful as well (convergence, # iterations, etc.), along with an indication that the solver is running (so that he user isn't staring at a static screen, wondering if the Solve softkey has been tapped successfully).