a) \((5 - 7i) + \sqrt 3 x = (2 - 5i)(1 + 3i)\)\( \Leftrightarrow \sqrt 3 x = \left( {2 - 5i} \right)\left( {1 + 3i} \right) - 5 + 7i\)
\( \Leftrightarrow \sqrt 3 x = 2 - 5i + 6i + 15 - 5 + 7i\) \( \Leftrightarrow \sqrt 3 x = 12 + 8i\) \( \Leftrightarrow x = \dfrac{{12}}{{\sqrt 3 }} + \dfrac{8}{{\sqrt 3 }}i\)
b) \(5 - 2ix = \left( {3 + 4i} \right)\left( {1 - 3i} \right)\) \( \Leftrightarrow 5 - 2ix = 3 + 4i - 9i + 12\) \( \Leftrightarrow 5 - 2ix = 15 - 5i\)
\( \Leftrightarrow 2ix = - 10 + 5i\) \( \Leftrightarrow x = \dfrac{{ - 10 + 5i}}{{2i}} = \dfrac{{ - 10i - 5}}{{ - 2}}\) \( \Leftrightarrow x = \dfrac{5}{2} + 5i\)
