Complex Numbers And Quadratic Equations question 823
Question: If $ {{(-7-24i)}^{1/2}}=x-iy, $ then $ x^{2}+y^{2}= $ [RPET 1989]
Options:
A) 15
B) 25
C) - 25
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \sqrt{-7-24i}=x-iy $ Squaring both sides, $ -7-24i=x^{2}-y^{2}-i(2xy) $ Equating real and imaginary parts, we get $ x^{2}-y^{2}=-7 $ and $ 2xy=24 $
$ \therefore x^{2}+y^{2}=\sqrt{49+576}=\sqrt{625}=25 $
BETA
