Complex Numbers And Quadratic Equations question 654
Question: If the point $ z_1=1+i $ where $ i=\sqrt{-1} $ is the reflection of a point $ z_2=x+iy $ in the line $ i\bar{z}-iz=5, $ then the point $ z_2 $ is
Options:
A) $ 1+4i $
B) $ 4+i $
C) $ 1-i $
D) $ -1-i $
Show Answer
Answer:
Correct Answer: A
Solution:
$ Let z=a+bi $
$ \Rightarrow \bar{z} = a- bi $
$ \therefore i\bar{z}-iz=i[(a-bi)-(a+bi)]1=5 $
$ \Rightarrow i[ -2bi ]=5 $
$ \Rightarrow b=\frac{5}{2} $ So from figure it is clear that $ x=1,y=\frac{5}{2}+\frac{3}{2}=4 $ $ z_2=1+4i $
BETA
