gradef(g(u,v),g_u(u,v),g_v(u,v));
gradef(u(x,y),u_x(x,y),u_y(x,y))$
gradef(v(x,y),v_x(x,y),v_y(x,y))$
f(x,y):=g(u(x,y),v(x,y));
D:diff(f(x,y),x)+%i*diff(f(x,y),y);
E:divide(D,g_u(u(x,y),v(x,y))+%i*g_v(u(x,y),v(x,y)),g_u(u(x,y),v(x,y)));
F:divide(E[2],g_v(u(x,y),v(x,y)));
/*
    [%i v_y(x, y) + v_x(x, y) + u_y(x, y) - %i u_x(x, y), 0]
*/
F[1]+%i*(u_x(x,y)+%i*v_x(x,y)+%i*(v_x(x,y)+%i*(v_y(x,y))));
