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4-1.Complex numbers
hard
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 $\left| {\begin{array}{*{20}{c}}a&b&c\\b&c&a\\c&a&b\end{array}} \right| = 0$, 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
$arg\left( {\frac{{{z_3} - {z_1}}}{{{z_2} - {z_1}}}} \right)$
Solution
(c)First deduce that $a = b = c$, then it will be equal to $arg{\left( {\frac{{{z_3} – {z_1}}}{{{z_2} – {z_1}}}} \right)^2}$.
Standard 11
Mathematics
