Complex Numbers And Quadratic Equations question 421
Question: The real values of $ x $ and $ y $ for which the equation is $ (x+iy) $ $ (2-3i) $ = $ 4+i $ is satisfied, are [Roorkee 1978]
Options:
A) $ x=\frac{5}{13},y=\frac{8}{13} $
B) $ x=\frac{8}{13},y=\frac{5}{13} $
C) $ x=\frac{5}{13},y=\frac{14}{13} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Equation $ (x+iy)(2-3i)=4+i $
Þ $ (2x+3y)+i(-3x+2y)=4+i $ Equating real and imaginary parts, we get $ 2x+3y=4 $ ……(i) $ -3x+2y=1 $ ……(ii) From (i) and (ii), we get $ x=\frac{5}{13},y=\frac{14}{13} $ Aliter: $ x+iy=\frac{4+i}{2-3i}=\frac{(4+i)(2+3i)}{13}=\frac{5}{13}+\frac{14}{13}i $ .
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