Can Mathematica reduce this inequality into a domain of z
, where {z
, r1
, r2
} are all complex?
Reduce[Abs[z^2 - r1] > Abs[z^3 - r2], z]
The line never returns a result. I also tried just calculating the boundary:
Simplify[Abs[z^2 - r1] == Abs[z^3 - r2]]
But that never returns a result either. I've tried a few other methods that all just crashed or failed. I found a related Question and another related Question but I couldn't figure out how to apply those partial solutions to this problem.
BTW, I realize Solve[]
and Reduce[]
don't cope with Abs[]
. Even this simpler command give a poor result:
Simplify[Abs[z^2] == Abs[z^3]];
(* Abs[z]^2 == Abs[z] *)
And just to be clear, I don't just need the answer to the inequality, I need to know how to make Mathematica do it.
Reduce
you're working over the reals:Reduce[Abs[z^2 - r1] > Abs[z^3 - r2], z, Reals]
. $\endgroup$tick
marks in the title aren't being turned into niceFont
? $\endgroup$Simplify[Abs[z^2] == Abs[z^3]]
should return? Keep in mindz
is considered complex unless otherwise stated. $\endgroup$