Số phức sau đây \(z = \dfrac{{3 + 4i}}{{2 + 3i}} + \dfrac{{5 - 2i}}{{2 - 3i}}\) bằng:

* Hướng dẫn giải

\(\begin{array}{l}z = \dfrac{{3 + 4i}}{{2 + 3i}} + \dfrac{{5 - 2i}}{{2 - 3i}}\\\,\,\,\, = \dfrac{{\left( {3 + 4i} \right)\left( {2 - 3i} \right) + \left( {5 - 2i} \right)\left( {2 + 3i} \right)}}{{4 - 9{i^2}}}\\\,\,\,\, = \dfrac{{6 - i - 12{i^2} + 10 + 11i - 6{i^2}}}{{13}}\\\,\,\,\, = \dfrac{{34}}{{13}} + \dfrac{{10}}{{13}}i\end{array}\)