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Question

If $z_{1}, z_{2}, z_{3}$ be three non-zero complex number, such that $z_{2} \neq z_{1}, a = | z_{1} |, b = | z_{2} | a n d c = | z_{3} |$ suppose that
$∣ ∣ ∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣ ∣ ∣ = 0, t h e n a r g (\frac{z_{3}}{z_{2}})$ is equal to

A

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B

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C

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D

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Solution

The correct option is C
First deduce that a = b = c, then it will be equal to $a r g {(\frac{z_{3} - z_{1}}{z_{2} - z_{1}})}^{2}$ .

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∣ ∣ ∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣ ∣ ∣ = 0

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