A) 0
B) \[\frac{\pi }{2}\]
C) \[\frac{3\pi }{2}\]
D) \[\pi \]
Correct Answer: A
Solution :
We have \[{{z}_{2}}={{\overline{z}}_{1}}\]and \[{{z}_{4}}={{\overline{z}}_{3}}\] Therefore \[{{z}_{1}}{{z}_{2}}=|{{z}_{1}}{{|}^{2}}\]and \[{{z}_{3}}{{z}_{4}}=|{{z}_{3}}{{|}^{2}}\] Now \[arg\left( \frac{{{z}_{1}}}{{{z}_{4}}} \right)+arg\left( \frac{{{z}_{2}}}{{{z}_{3}}} \right)=arg\left( \frac{{{z}_{1}}{{z}_{2}}}{{{z}_{4}}{{z}_{3}}} \right)\] \[=arg\left( \frac{|{{z}_{1}}{{|}^{2}}}{|{{z}_{3}}{{|}^{2}}} \right)=arg\left( {{\left| \frac{{{z}_{1}}}{{{z}_{3}}} \right|}^{2}} \right)\]= 0 (\[\because \]Argument of positive real number is zero).
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