• # question_answer If ${{z}_{1}},{{z}_{2}},{{z}_{3}}$be three non-zero complex number, such that ${{z}_{2}}\ne {{z}_{1}},a=|{{z}_{1}}|,b=|{{z}_{2}}|$ and $c=|{{z}_{3}}|$ suppose that $\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix} \right|=0$, then  $arg\left( \frac{{{z}_{3}}}{{{z}_{2}}} \right)$ is equal to A) $arg{{\left( \frac{{{z}_{2}}-{{z}_{1}}}{{{z}_{3}}-{{z}_{1}}} \right)}^{2}}$ B) $arg\left( \frac{{{z}_{2}}-{{z}_{1}}}{{{z}_{3}}-{{z}_{1}}} \right)$ C) $arg{{\left( \frac{{{z}_{3}}-{{z}_{1}}}{{{z}_{2}}-{{z}_{1}}} \right)}^{2}}$ D) $arg\left( \frac{{{z}_{3}}-{{z}_{1}}}{{{z}_{2}}-{{z}_{1}}} \right)$

First deduce that$a=b=c$, then it will be equal to$arg{{\left( \frac{{{z}_{3}}-{{z}_{1}}}{{{z}_{2}}-{{z}_{1}}} \right)}^{2}}$.