MATLAB: Interpretation of output of solve()

complex numbersequationsnot linearsolve

Hi everybody
Brief descirption of my situation: Two equations, 2 unknown variables (R, I) I want two equations for I=? and R=?
First equation:
I^2*(448-x)+R^2*(x-448)-2*x*R-x+448==0
Second equation:
I^2*y+I*896+R^2*y+2*y*R+y == 0
Unknowns are I and R.
I´ve tried the following:
syms I R x y
[solI, solR] = solve([I^2*(448-x)+R^2*(x-448)-2*x*R-x+448==0, I^2*y+I*896+R^2*y+2*y*R+y == 0], [I, R]);
This outputs me (for solR):
RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[1]
RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[2]
RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[3]
RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[4]
and (for solI):
(y*RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[1])/(x - 448) - (y*RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[1]^2)/448
(y*RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[2])/(x - 448) - (y*RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[2]^2)/448
(y*RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[3])/(x - 448) - (y*RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[3]^2)/448
(y*RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[4])/(x - 448) - (y*RootOf(896*x*y^2*z^4 - x^2*y^2*z^4 - 200704*y^2*z^4 + 896*x*y^2*z^3 - 401408*y^2*z^3 - 179830784*x*z^2 - 200704*y^2*z^2 + 200704*x^2*z^2 + 40282095616*z^2 - 401408*x^2*z + 179830784*x*z + 179830784*x - 200704*x^2 - 40282095616, z)[4]^2)/448
Here my questions: 1. I tried to understand what has been explained here. I still don´t understand what I have to use the z for. 2. The output show [1], [2], [3] and [4] in middle of those solutions. What is this for? How should I interpret this?
I am grateful for everyone helping me.
Thank you in advance.

Best Answer

You have a system of two equations in two unknowns, but with coefficients that are also symbolic. Usually this is a system that has no analytical solution. Wanting one to exist does not always suffice.
Nothing stops you from trying vpa(solI). However here that yields a big mess. There is no magic.
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