Re: FindRoot[] with mixed complex and real variables?

*To*: mathgroup at smc.vnet.net*Subject*: [mg79643] Re: FindRoot[] with mixed complex and real variables?*From*: chuck009 <dmilioto at comcast.com>*Date*: Wed, 1 Aug 2007 04:55:25 -0400 (EDT)

Ok, ok. I was wrong. How about coding it as 7 variables in 7 unknowns (the two equations in terms of u, v and w, then the same two equations in terms x, y, t and s (that's 4, then these three: u=x+iy w=it g=-200+is Alright, that's seven. Then use FindRoot with your starting values: FindRoot[{(x + I*y)*BesselJ[1, x + I*y]*BesselK[0, I*t] == I*t*BesselK[1, I*t]*BesselJ[0, x + I*y], (x + I*y)^2 - t^2 == -200 + I*s, u*BesselJ[1, u]*BesselK[0, w] == w*BesselK[1, w]* BesselJ[0, u], u^2 + w^2 == g, u == x + I*y, w == I*t, g == -200 + I*s}, {{x, -2.39}, {y, 0.8}, {t, 14.34}, {s, 0.8}, {u, 2.39 + 0.17*I}, {g, -200 + 0.8*I}, {w, 14.34*I}}] when I do that, I get the following solutions: {x -> -2.389999999999996 + 1.7419722275807886*^-15*I, y -> 0.7999999999999983 + 3.775812800225189*^-15*I, t -> 14.34 + 8.01608452040757*^-24*I, s -> 0.8 + 4.257789892107953*^-22*I, u -> 2.39 + 0.17*I, g -> -200. + 0.8*I, w -> -8.016084539066267*^-24 + 14.34*I} > Yes -- besides the two initial complex-valued > equations, there are the > two real constraints: Re[w]==0 and Re[g]==(a > fixed & stated value). > > So, there's enough info to solve the problem, and I > can indeed get > answers in other ways. My problem is how to get this > info into > FindRoot[]. >