Complex Numbers And Quadratic Equations question 824
Question: If $ \sqrt{x+iy}=\pm (a+ib), $ then $ \sqrt{-x-iy} $ is equal to
Options:
A) $ \pm (b+ia) $
B) $ \pm (a-ib) $
C) $ \pm (b-ia) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \sqrt{x+iy}=\pm (a+bi) $
Þ $ x+iy=a^{2}-b^{2}+2iab $
Þ $ x=a^{2}-b^{2}, $ $ y=2ab $ \ $ \sqrt{-x-iy}=\sqrt{-(a^{2}-b^{2})-2iab}=\sqrt{b^{2}-a^{2}-2iab} $ $ =\sqrt{{{(b-ia)}^{2}}}=\pm (b-ia) $ .
BETA
