Complex Numbers And Quadratic Equations question 422
Question: The real values of $ x $ and $ y $ for which the equation $ (x^{4}+2xi)-(3x^{2}+yi)= $ $ (3-5i)+(1+2yi) $ is satisfied, are [Roorkee 1984]
Options:
A) $ x=2,y=3 $
B) $ x=-2,y=\frac{1}{3} $
C) Both (a) and (b)
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Given equation $ (x^{4}+2xi)-(3x^{2}+yi)=(3-5i)+(1+2yi) $
$ \Rightarrow (x^{4}-3x^{2})+i(2x-3y)=4-5i $ Equating real and imaginary parts, we get $ x^{4}-3x^{2}=4 $ ……(i) and $ 2x-3y=-5 $ …..(ii) From (i) and (ii), we get $ x=\pm 2 $ and $ y=3,\frac{1}{3} $ Trick: Put $ x=2,y=3 $ and then $ x=-2, $ $ y=\frac{1}{3}, $ we see that they both satisfy the given equation.
BETA
