Complex Numbers And Quadratic Equations question 123
Question: If $ (3+i)z=(3-i)\bar{z}, $ then complex number z is [AMU 2005]
Options:
A) $ x(3-i),x\in R $
B) $ \frac{x}{3+i},x\in R $
C) $ x(3+i),x\in R $
D) $ x(-3+i),x\in R $
Show Answer
Answer:
Correct Answer: A
Solution:
Given: $ (3+i)z=(3-i)\bar{z} $ Let $ z=x(3-i) $ , $ x\in R $ L.H.S. = $ (3+i)z $ = $ (3+i)x(3-i) $ = $ x(3+i)(3-i)=x[{{(3)}^{2}}+1^{2}]=10x $ R.H.S. = $ (3-i)\bar{z}=(3-i)x(3+i)=x[3^{2}+1^{2}]=10x $ Hence, L.H.S. = R.H.S. $ \because $ $ z=x(3-i) $ satisfies the equation, then $ z=x(3-i) $ , where x is a real number.
BETA
