Cho hai số phức \(z_1\) và \(z_2\) thỏa mãn \({z_2...

A

- Hướng dẫn giải

Do \({z_2} \ne 0;\,\,{z_1} + {z_2} \ne 0\) ta có

\(\begin{array}{l}\frac{{{z_1}}}{{{z_1} + {z_2}}} = 1 + \frac{{2{z_1}}}{{{z_2}}} \Leftrightarrow {z_1}.{z_2} + 2{z_1}^2 + {z_2}^2 + 2{z_1}{z_2} \Leftrightarrow 2{z_1}^2 + {z_2}^2 + 2{z_1}.{z_2} = 0\\ \Leftrightarrow 2{\left( {\frac{{{z_1}}}{{{z_2}}}} \right)^2} + 2\frac{{{z_1}}}{{{z_2}}} + 1 = 0 \Leftrightarrow \left[ \begin{array}{l}\frac{{{z_1}}}{{{z_2}}} = - \frac{1}{2} + \frac{1}{2}i\\\frac{{{z_1}}}{{{z_2}}} = - \frac{1}{2} - \frac{1}{2}i\end{array} \right. \Rightarrow \left| {\frac{{{z_1}}}{{{z_2}}}} \right| = \frac{{\sqrt 2 }}{2}\end{array}\)