# How to deal with complex equations in Solve method?

I am trying to deal with complex equations to solve them and use them in the plot. I want to know why these equations are not being solved.

sol = Solve[{3*I*x1 + 2*y1 + 5*z1*Abs[x1] + U1 == 0,
6*Conjugate[y1] - 4*Abs[z1] + 8*x1 + U1 == 0,
3*Conjugate[z1] + 9*y1 - 5*x1 - U1 == 0}, {x1, y1, z1}];
Plot[{Evaluate[Conjugate[x1]*x1] /. sol}, {U1, 0, 3}]


When I am running the program it is continuously running.

• Worst comes to worst, you could try rewriting in terms of explicit real and imaginary parts. Commented May 19, 2020 at 11:46
• Solve tends to be pretty good at polynomial problems and sometimes not so good at other kinds of problems. You might try using Reduce and see what it can do, but I don't hold out much hope for the size and complexity of problems that you are looking for solutions to, particularly if you are expecting answers in a few moments or minutes or even hours.
– Bill
Commented May 19, 2020 at 15:30
• You can get a glimpse of the solution's horrendous complexity by setting U1 = 1. This particular case can be solved instantly, and the result doesn't look that bad due to all the guts being neatly hidden inside the AlgebraicNumber containers. Hover your mouse above them. Yet, Mathematica still hides from view most of what can be seen with InputForm - if you are brave enough. Now, the complete solution is unimaginably worse, way beyond human and machine comprehension altogether. Commented May 19, 2020 at 17:40