Question

calculati conjugatul numarului complex z=(1+2i)(2-i)

Answer 1

[tex]z=\frac{1+2i}{2-i}\\ \overline{z}=\overline{(\frac{1+2i}{2-i})}=\frac{\overline{1+2i}}{\overline{2-i}}=\frac{1-2i}{2+i}=\frac{(1-2i)(2-i)}{(2+i)(2-i)}=\frac{2-i-4i+2}{4+1}\\ =\frac{4-5i}{5}=\frac{4}{5}-i[/tex]