Question

z+2zconjugado=6+5i
Número complexo

Answer 1

$\mathrm{\Rightarrow Z=a+bi\ \ \|\ \ \Rightarrow \overline{Z}=a-bi}\\\\ \mathrm{Z+2\overline{Z}=6+5i\ \to\ a+bi+2(a-bi)=6+5i}\\ \mathrm{a+bi+2a-2bi=6+5i\ \to\ 3a-bi=6+5i}\\\\ \mathrm{\Rightarrow \Re{(Z)}=\Re{(Z)}\ \to\ 3a=6\ \to\ \boxed{\mathrm{a=2}}}\\ \mathrm{\Rightarrow \Im{(Z)}=\Im{(Z)}\ \to\ -b=5\ \to\ \boxed{\mathrm{b=-5}}}\\\\ \mathrm{Z=a+bi\ \to\ \boxed{\boxed{\mathbf{Z=2-5i}}}}$