Question: The value of $(z+3)(\bar{z}+3)$ is equivalent to
(a) $|z+3|^{2}$
(b) $|z-3|$
(c) $z^{2}+3$
(d) none of these
Solution:
Since $|z+3|^{2}$
$=(z+3)(\overline{z+3})$
$=(z+3)(\bar{z}+3)$ $(\because \overline{3}=3$ real $)$
$=(z+3)(\bar{z}+3)$
Hence, the correct answer is option A.
