Complex Numbers And Quadratic Equations question 407
Question: The values of $ x $ and $ y $ satisfying the equation $ \frac{(1+i)x-2i}{3+i} $ $ +\frac{(2-3i)y+i}{3-i}=i $ are [IIT 1980; MNR 1987]
Options:
A) $ x=-1,y=3 $
B) $ x=3,y=-1 $
C) $ x=0,y=1 $
D) $ x=1,y=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i $
Þ $ (4+2i)x+(9-7i)y-3i-3=10i $ Equating real and imaginary parts, we get $ 2x-7y=13 $ and $ 4x+9y=3 $ . Hence $ x=3 $ and $ y=-1 $ . Trick : After finding the equations, no need to solve them, put the values of $ x $ and $ y $ given in the options and get the appropriate option.
BETA
