Giải bài 2 trang 133 – SGK môn Giải tích lớp 12

Hướng dẫn:

Cho hai số phức $z=a+bi$ và $z'=a'+b'i$. Khi đó $z=z'\Leftrightarrow \left\{\begin{align} &a=a'\\&b=b'\\ \end{align}\right.$.

a) $\left( 3x-2 \right)+\left( 2y+1 \right)i=\left( x+1 \right)-\left( y-5 \right)i$

$\Leftrightarrow\left\{ \begin{aligned} & 3x-2=x+1 \\ & 2y+1=-\left( y-5 \right) \\ \end{aligned} \right. \\ \Leftrightarrow \left\{ \begin{aligned} & x=\dfrac{3}{2} \\ & y=\dfrac{4}{3} \\ \end{aligned} \right.$

b) $\left( 1-2x \right)-i\sqrt{3}=\sqrt{5}+\left( 1-3y \right)i$

$\Leftrightarrow \left\{ \begin{aligned} & 1-2x=\sqrt{5} \\ & -\sqrt{3}=1-3y \\ \end{aligned} \right. \\ \Leftrightarrow \left\{ \begin{aligned} & x=\dfrac{1-\sqrt{5}}{2} \\ & y=\dfrac{1+\sqrt{3}}{3} \\ \end{aligned} \right.$

c) $\left( 2x+y \right)+\left( 2y-x \right)i=\left( x-2y+3 \right)+\left( y+2x+1 \right)i$

$\Leftrightarrow\left\{ \begin{aligned} & 2x+y=x-2y+3 \\ & 2y-x=y+2x+1 \\ \end{aligned} \right. \\ \Leftrightarrow \left\{ \begin{aligned} & x+3y=3 \\ & 3x-y=-1 \\ \end{aligned} \right. \\ \Leftrightarrow \left\{ \begin{aligned} & x=0 \\ & y=1 \\ \end{aligned} \right.$