Complex Numbers And Quadratic Equations question 821
Question: If $ x+iy=\sqrt{\frac{a+ib}{c+id}}, $ then $ {{(x^{2}+y^{2})}^{2}}= $ [IIT 1979; RPET 1997; Karnataka CET 1999]
Options:
A) $ \frac{a^{2}+b^{2}}{c^{2}+d^{2}} $
B) $ \frac{a+b}{c+d} $
C) $ \frac{c^{2}+d^{2}}{a^{2}+b^{2}} $
D) $ {{( \frac{a^{2}+b^{2}}{c^{2}+d^{2}} )}^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ x+iy=\sqrt{\frac{a+ib}{c+id}} $
Þ $ x-iy=\sqrt{\frac{a-ib}{c-id}} $ Also $ x^{2}+y^{2}=(x+iy)(x-iy)=\sqrt{\frac{a^{2}+b^{2}}{c^{2}+d^{2}}} $
Þ $ {{(x^{2}+y^{2})}^{2}}=\frac{a^{2}+b^{2}}{c^{2}+d^{2}} $
BETA
