Question

If $z$ is a complex number then $(z+5)(\overline{z}+5)$ is

• A. $(z+5{)}^2$
• B. $|z+5{|}^2$
• C. $|z+5i{|}^2$
• D. $|z-5{|}^2$

Answer 1

The correct option is B $|z+5{|}^2$

If z is a complex number then
$(z+5)(\overline{z}+5)=(z+5)\overline{(z+5)}=|z+5{|}^2[\because z\overline{z}=|z{|}^2]$