Đáp án:
`|z|=3/sqrt10`
Giải thích các bước giải:
$\begin{array}{l} \frac{{1 + 2i}}{{\overline z }} = \frac{{\left( {1 - i} \right).z}}{{{{\left| z \right|}^2}}} + 1 + 3i\\ \Leftrightarrow \frac{{1 + 2i}}{{\overline z }} = \frac{{\left( {1 - i} \right).z}}{{z.\overline z }} + 1 + 3i\\ \Leftrightarrow \frac{{1 + 2i}}{{\overline z }} = \frac{{1 - i}}{{\overline z }} + 1 + 3i\\ \Leftrightarrow \frac{{1 + 2i}}{{\overline z }} - \frac{{1 - i}}{{\overline z }} = 1 + 3i\\ \Leftrightarrow \frac{{1 + 2i - 1 + i}}{{\overline z }} = 1 + 3i\\ \Leftrightarrow \frac{{3i}}{{\overline z }} = 1 + 3i\\ \Leftrightarrow \left| {\frac{{3i}}{{\overline z }}} \right| = \left| {1 + 3i} \right|\\ \Leftrightarrow \frac{{\left| {3i} \right|}}{{\left| {\overline z } \right|}} = \sqrt {{1^2} + {3^2}} \\ \Leftrightarrow \frac{3}{{\left| z \right|}} = \sqrt {10} \\ \Leftrightarrow \left| z \right| = \frac{3}{{\sqrt {10} }} \end{array}$
