Complex Numbers And Quadratic Equations question 122
Question: If $ z_1=1+2i $ and $ z_2=3+5i $ , and then $ Re( \frac{{{{\bar{z}}}_2}z_1}{z_2} ) $ is equal to [J & K 2005]
Options:
A) $ \frac{-31}{17} $
B) $ \frac{17}{22} $
C) $ \frac{-17}{31} $
D) $ \frac{22}{17} $
Show Answer
Answer:
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 $ Re( \frac{{{{\bar{z}}}_2}z_1}{z_2} )=\frac{44}{34}=\frac{22}{17} $ .
BETA
