A) \[\frac{-31}{17}\]
B) \[\frac{17}{22}\]
C) \[\frac{-17}{31}\]
D) \[\frac{22}{17}\]
Correct Answer: D
Solution :
Given\[{{z}_{1}}=1+2i\], \[{{z}_{2}}=3+5i\] and \[{{\bar{z}}_{2}}=3-5i\] \[\frac{{{{\bar{z}}}_{2}}{{z}_{1}}}{{{z}_{2}}}=\frac{(3-5i)\,(1+2i)}{(3+5i)}=\frac{13+i}{3+5i}\] = \[\frac{13+i}{3+5i}\times \frac{3-5i}{3-5i}=\frac{44-62i}{34}\] Then\[\operatorname{Re}\left( \frac{{{{\bar{z}}}_{2}}{{z}_{1}}}{{{z}_{2}}} \right)=\frac{44}{34}=\frac{22}{17}\].
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