Răspuns:
Fie z = [tex]a+bi[/tex]
[tex]=>(a+bi)^2+2(a-bi)+1=0[/tex]
[tex]<=>a^2-b^2+2abi+2a-2bi+1=0=>a^2-b^2+2a+1=0[/tex]
si [tex]2ab-2b=0=>2b(a-1)=0[/tex]
[tex]Caz 1: b=0=>a^2-0+2a+1=0=>a=-1 =>z1=-1[/tex]
[tex]Caz 2:a=1=>1-b^2+2+1=0>b^2=-4=>b=[/tex]±[tex]2i=> z2=1+2i[/tex]
[tex]z3=1-2i[/tex]
