Complex Numbers And Quadratic Equations question 433
Question: If $ \frac{3x+2iy}{5i-2}=\frac{15}{8x+3iy} $ , then
Options:
A) $ x=1,y=-3 $
B) $ x=-1,y=3 $
C) $ x=1,y=3 $
D) $ x=-1,y=-3 $ or $ x=1, $ $ y=3 $
Show Answer
Answer:
Correct Answer: D
Solution:
Given that $ \frac{3x+2iy}{5i-2}=\frac{15}{8x+3iy} $
Þ $ 24x^{2}+9ixy-6y^{2}+16ixy=75i-30 $
Þ $ 24x^{2}-6y^{2}+25ixy=75i-30 $ Equating real and imaginary parts, we get $ 24x^{2}-6y^{2}=-30 $ or $ 4x^{2}-y^{2}=-5 $ and $ xy=3 $ On solving we get $ x=\pm 1,y=\pm 3 $
BETA
