Bài tập 4.20 trang 204 SBT Toán 12

a)

\(\begin{array}{l}
\left( {3 + 4i} \right)x = \left( {1 + 2i} \right)\left( {4 + i} \right)\\
 \Leftrightarrow (3 + 4i)x = 2 + 9i\\
 \Leftrightarrow x = \frac{{2 + 9i}}{{3 + 4i}}\\
 \Leftrightarrow x = \frac{{(2 + 9i)(3 - 4i)}}{{25}}\\
 \Leftrightarrow x = \frac{{42}}{{25}} + \frac{{19}}{{25}}i
\end{array}\)

b) 

\(\begin{array}{l}
2ix + 3 = 5x + 4i\\
 \Leftrightarrow (5 - 2i)x = 3 - 4i\\
 \Leftrightarrow x = \frac{{3 - 4i}}{{5 - 2i}} = \frac{{(3 - 4i)(5 + 2i)}}{{25 + 4}}\\
 \Leftrightarrow x = \frac{{23}}{{29}} - \frac{{14}}{{29}}i
\end{array}\)

c)

\(\begin{array}{l}
3x\left( {2 - i} \right) + 1 = 2ix\left( {1 + i} \right) + 3i\\
 \Leftrightarrow [3(2 - i) - 2i(1 + i)]x =  - 1 + 3i\\
 \Leftrightarrow (8 - 5i)x =  - 1 + 3i\\
 \Leftrightarrow x = \frac{{ - 1 + 3i}}{{7 - 5i}} =  - \frac{{23}}{{89}} + \frac{{19}}{{89}}i
\end{array}\)

-- Mod Toán 12 HỌC247