[tex]\displaystyle |z|= \left| \frac{1+xi}{2-xi} \right|= \frac{|1+xi|}{|2-xi|}= \frac{\sqrt{x^2+1}}{\sqrt{x^2+4}}= \sqrt{\frac{x^2+1}{x^2+4}}. \\ \\ |z|\ \textless \ 1 \Leftrightarrow \sqrt{\frac{x^2+1}{x^2+4}} \ \textless \ 1. \\ \\ Cum~ \sqrt{\frac{x^2+1}{x^2+4}} \geq 0,~iar~1\ \textgreater \ 0,~putem~ridica~ultima~relatie~la~ \\ \\ patrat,~obtinand~ \frac{x^2+1}{x^2+4}\ \textless \ 1. \\ \\ Aceasta~ultima~relatie~este~adevarata~\forall~x \in \mathbb{R},~deoarece \\ \\ 0\ \textless \ x^2+1\ \textless \ x^2+4. \\ \\ Deci~S= \mathbb{R}.[/tex]
