question_answer

If \[{{z}_{1}},\] \[{{z}_{2}}\] are two complex numbers such that \[\left| \frac{{{z}_{1}}-{{z}_{2}}}{{{z}_{1}}+{{z}_{2}}} \right|=1\] and \[i{{z}_{1}}=k{{z}_{2}},\] where \[K\in R,\] then the angle between \[{{z}_{1}}-{{z}_{2}}\] and \[{{z}_{1}}+{{z}_{2}}\] is

A)  \[{{\tan }^{-1}}\left( \frac{2k}{{{k}^{2}}+1} \right)\] 

B)  \[{{\tan }^{-1}}\left( \frac{2k}{1-{{k}^{2}}} \right)\]

C)  \[-2{{\tan }^{-1}}k\]   

D)  \[2{{\tan }^{-1}}k\]

E)  None of these