Question

Determinati partea reala a numarului Z = (3+2i)/(2+i)

Answer 1

[tex]\frac{3+2i}{2+i}=\frac{(3+2i)(2-i)}{(2+i)(2-i)}=\frac{6+4i-3i-2i^2}{2^2-i^2}=\\ \frac{8+i}{4+1}=\frac{8+i}{5}=\frac{8}{5}+\frac{i}{5}\\ Re(\frac{3+2i}{2+i})=Re(\frac{8}{5}+\frac{i}{5})=\frac{8}{5}[/tex]