# Resolution of equations – An optimization problem.

I have the following two quantities denoted by $$LHS$$ Y $$RHS$$

``````    LHS = Abs[
p1 (z12 - z21) + I p2 (z12 - z21) + p3 (z11 - z22) + q (z11 + z22)];
RHS = Sqrt[Abs[z11]^ 2 + Abs[z21]^ 2]+ Sqrt[Abs[z12]^ 2 + Abs[z22]^ 2];
``````

Here, $$zij$$ ($$i, j = 1.2$$) are complex numbers. I need to find the values ​​of $$p1, p2, p3$$ Y $$q$$, such that $$LHS> RHS$$, subject to the condition that $$| q | + | vec {p} | le 1$$, where $$vec {p} = (p1, p2, p3)$$.

This is my first question about Mathe-SE, sorry if you find the problem trivial or inappropriate in the description.