Question

If $z$ is a complex number, then the conjugate of $z+2\overline{z}$ is

• A. $2\overline{z}+z$
• B. $\overline{z}+2z$
• C. $\overline{z}-2z$
• D. $2\overline{z}-z$

Answer 1

The correct option is B $\overline{z}+2z$

By property of conjugates, we know that,
$[\overline{z_1+z_2}=\overline{z_1}+\overline{z_2}]$
$\therefore \overline{(z+2\overline{z})}=\overline{z}+\overline{\left(2\overline{z}\right)}=\overline{z}+2\overline{\overline{z}}[\because \overline{\left(z_1{z}_2\right)}=\overline{z_1}\overline{z_2},\overline{2}=2]=\overline{z}+2z[\because \overline{\overline{z}}=z]$