drawing phase portrait given phase and magnitude (not ODEs)

I'm trying to plot the arrows in a 2D plane that corresponding to the complex number

f(x,y) = f0(x,y)e^(-i*phi(x,y))

Now, I know how to use quiver(x,y,u,v) if I had, say a 2D ode system, xdot = y and ydot = v, but I'm not sure how to go about doing it if I just have the magnitude and phase of a complex number.

For instance let's say f0(x,y) = 1 and I have a function phi(x,y) = h(x)*x+ g(y)*y, how would I use quiver to accomplish a 2D phase portrait?

I don't think the following works, does it?

[x,y] = meshgrid(-1:0.1:1,-1:0.1:1);
u = g(x)*x;
v = h(y)*y;
quiver(x,y,u,v)

Would appreciate any help, thanks in advance!