Un numar complex z este numar real⇔z=conjugatul nr z
[tex]z=\overline{z}<=> \frac{a+2i}{2+ai} =\frac{a-2i}{2-ai}<=>\\
(a+2i)(2-ai)=(2+ai)(a-2i)\\
2a-2ai+4i+2a=2a-4i+a^2i+2a\\
4a+i(-2a+4)=4a+i(-4+a^2)\\
-2a+4=-4+a^2\\
a^2+2a-8=0\\
\triangle=4+23=36\\
a_{1/2}= \frac{-2\pm6}{2} \\
a_1=2\\
a_2=-4
[/tex]
