If \(a=\frac{1-i \sqrt{3}}{2}\), then the correct matching of 'List-I from List-II is
List-I
List-II
(i) \(a \bar{a}\)
(A) \(-\frac{\pi}{3}\)
(ii) \(\arg \left(\frac{1}{\bar{a}}\right)\)
(B) \(-i \sqrt{3}\)
(iii) \(a-\bar{a}\)
(C) \(2 i / \sqrt{3}\)
(iv) \(\operatorname{Im}\left(\frac{4}{3 a}\right)\)
(D) 1
(E) \(\pi / 3\)
(F) \(\frac{2}{\sqrt{3}}\)
correct match is
(i)
(ii)
(iii)
(iv)

1. A \(\begin{array}{llll}D & \text { E } & \text { C } & \text { B }\end{array}\)
2. B \(\begin{array}{llll}\mathrm{D} & \mathrm{A} & \mathrm{B} & \mathrm{F}\end{array}\)
3. C \(\begin{array}{llll}\text { F } & \text { E } & \text { B } & \text { C }\end{array}\)
4. D \(\begin{array}{llll}D & A & B & C\end{array}\)