Đáp án:
$9\sqrt3 - 3\sqrt2$
Giải thích các bước giải:
$\quad \begin{cases}z_1 = 3 - \sqrt2i\\z_2 = \sqrt3 + 3i\end{cases}$
$\Rightarrow \begin{cases}\overline{z_1}= 3 + \sqrt2i\\\overline{z_2}= \sqrt3 - 3i\end{cases}$
Ta được:
$\quad v = z_1\overline{z_2} + \overline{z_1}z_2 + z_1z_2$
$\to v = \left(3-\sqrt2i\right)\left(\sqrt3 - 3i\right) + \left(3 +\sqrt2i\right)\left(\sqrt3 + 3i\right) + \left(3 -\sqrt2i\right)\left(\sqrt3 + 3i\right)$
$\to v = 3\left(\sqrt3 -\sqrt2\right) - \left(9 +\sqrt6\right)i + 3\left(\sqrt3 -\sqrt2\right) + \left(9 +\sqrt6\right)i + 3\left(\sqrt3 +\sqrt2\right) + \left(9 -\sqrt6\right)i$
$\to v = 9\sqrt3 - 3\sqrt2 + \left(9-\sqrt6\right)i$
$\to \overline{v}= 9\sqrt3 - 3\sqrt2 - \left(9-\sqrt6\right)i$