\( z_{1}, z_{2} \) and \( z_{3} \) are three non-zero complex numbers such that \( z_{1} \neq z_...

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\( z_{1}, z_{2} \) and \( z_{3} \) are three non-zero complex numbers such that \( z_{1} \neq z_{2} \neq z_{3} \), and \( a=\left|z_{1}\right|, b=\left|z_{2}\right|, c=\left|z_{3}\right| \). If \( \left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|=0 \) then show that \( \arg \left(\frac{z_{3}}{z_{2}}\right)=\arg \left(\frac{z_{3}-z_{1}}{z_{2}-z_{1}}\right)^{2} \)
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