11th Class Mathematics Complex Numbers and Quadratic Equations Question Bank Critical Thinking

  • 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) \[arg\left( \frac{{{z}_{3}}-{{z}_{1}}}{{{z}_{2}}-{{z}_{1}}} \right)\]

    Correct Answer: C

    Solution :

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

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