a) \(\left( {3 + 4i} \right)x = \left( {1 + 2i} \right)\left( {4 + i} \right)\) \( \Leftrightarrow \left( {3 + 4i} \right)x = 2 + 9i\) \( \Leftrightarrow x = \dfrac{{2 + 9i}}{{3 + 4i}}\)
\( \Leftrightarrow x = \dfrac{{\left( {2 + 9i} \right)\left( {3 - 4i} \right)}}{{\left( {3 + 4i} \right)\left( {3 - 4i} \right)}}\) \( \Leftrightarrow x = \dfrac{{42 + 19i}}{{25}} = \dfrac{{42}}{{25}} + \dfrac{{19}}{{25}}i\)
b) \(2ix + 3 = 5x + 4i\) \( \Leftrightarrow \left( {5 - 2i} \right)x = 3 - 4i\) \( \Leftrightarrow x = \dfrac{{3 - 4i}}{{5 - 2i}}\) \( \Leftrightarrow x = \dfrac{{\left( {3 - 4i} \right)\left( {5 + 2i} \right)}}{{\left( {5 - 2i} \right)\left( {5 + 2i} \right)}}\) \( \Leftrightarrow x = \dfrac{{23 - 14i}}{{29}} = \dfrac{{23}}{{29}} - \dfrac{{14}}{{29}}i\)
c) \(3x\left( {2 - i} \right) + 1 = 2ix\left( {1 + i} \right) + 3i\) \( \Leftrightarrow x\left( {6 - 3i} \right) - x\left( {2i - 2} \right) = 3i - 1\) \( \Leftrightarrow x\left( {8 - 5i} \right) = - 1 + 3i\) \( \Leftrightarrow x = \dfrac{{ - 1 + 3i}}{{8 - 5i}}\) \( \Leftrightarrow x = \dfrac{{\left( { - 1 + 3i} \right)\left( {8 + 5i} \right)}}{{\left( {8 - 5i} \right)\left( {8 + 5i} \right)}}\)\( \Leftrightarrow x = \dfrac{{ - 23 + 19i}}{{89}} = - \dfrac{{23}}{{89}} + \dfrac{{19}}{{89}}i\)
