Giải bài 4.19 trang 204 - SBT Giải tích lớp 12
Thực hiện các phép tính sau :
\(\begin{align} & a)\,\dfrac{\left( 2+i \right)+\left( 1+i \right)\left( 4-3i \right)}{3+2i}; \\ & b)\dfrac{\left( 3-4i \right)\left( 1+2i \right)}{1-2i}+4-3i \\ \end{align} \)
Áp dụng:
\(\dfrac{a+bi}{c+di}=\dfrac{\left( a+bi \right)\left( c-di \right)}{{{c}^{2}}+{{d}^{2}}} \)
\(\begin{aligned}
& a)\,\dfrac{\left( 2+i \right)+\left( 1+i \right)\left( 4-3i \right)}{3+2i} \\
& =\dfrac{2+i+7+i}{3+2i} \\
& =\dfrac{9+2i}{3+2i} \\
& =\dfrac{\left( 9+2i \right)\left( 3-2i \right)}{9+4} \\
& =\dfrac{31-12i}{13}=\dfrac{31}{13}-\dfrac{12}{13}i; \\
& b)\dfrac{\left( 3-4i \right)\left( 1+2i \right)}{1-2i}+4-3i \\
& =\dfrac{11+2i}{1-2i}+4-3i \\
& =\dfrac{\left( 11+2i \right)\left( 1+2i \right)}{1+4}+4-3i \\
& =\dfrac{7+24i}{5}+4-3i \\
& =\dfrac{27}{5}+\dfrac{9}{5}i \\
\end{aligned} \)