Question

The value of $(z+3)(\overline{z}+3)$ is equivalent to

• A. $|z+3{|}^2$
• B. $|z-3|$
• C. $z^2+3$
• D. None of these

Answer 1

The correct option is A $|z+3{|}^2$

$(z+3)(\overline{z}+3)$

Let $z=x+iy$

$\overline{z}=x-iy$

$=\left(\right(x+3)+iy)\left(\right(x+3)-iy)$

$=(x+3{)}^2+y^2$

$=|z+3{|}^2$