Complex Numbers And Quadratic Equations question 826
Question: If $ \sqrt{a+ib}=x+iy $ , then possible value of $ \sqrt{a-ib} $ is [Kerala (Engg.) 2002]
Options:
A) $ x^{2}+y^{2} $
B) $ \sqrt{x^{2}+y^{2}} $
C) $ x+iy $
D) $ x-iy $
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Answer:
Correct Answer: D
Solution:
$ \sqrt{a+ib}=x+yi\Rightarrow {{( \sqrt{a+ib} )}^{2}}={{(x+yi)}^{2}} $
$ \Rightarrow a=x^{2}-y^{2},b=2xy $ and hence $ \sqrt{a-ib}=\sqrt{x^{2}-y^{2}-2xyi} $ $ =\sqrt{{{(x-yi)}^{2}}} $ $ =x-iy $ Note: In the question, it should have been given that $ a,b,x,y\in R. $
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