Question

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

(a) |z + 3|²

(b) |z – 3|

(c) z² + 3

(d) none of these

Answer 1

Since |z + 3|²

^{$$\begin{gathered} =\left(z+3\right)\left(\overline{z+3}\right) \\ =\left(z+3\right)\left(\overline{z}+3\right)\left(\because \overline{3}=3\mathrm{real}\right) \\ =\left(z+3\right)\left(\overline{z}+3\right) \end{gathered}$$}

Hence, the correct answer is option A.