A) \[\pm (b+ia)\]
B) \[\pm (a-ib)\]
C) \[(ai+b)\]
D) \[\pm (b-ia)\]
E) None of these
Correct Answer: D
Solution :
Given, \[\sqrt{x+iy}=\pm (a+bi)\] \[\Rightarrow \] \[x+iy={{a}^{2}}-{{b}^{2}}+2iab\] \[\Rightarrow \] \[x={{a}^{2}}-{{b}^{2}},y=2ab\] \[\therefore \,\,\,\,\sqrt{-x-iy}=\,\sqrt{-({{a}^{2}}-{{b}^{2}})-2\,iab}\] \[=\sqrt{{{b}^{2}}-{{a}^{2}}-2iab}\,=\sqrt{{{(b-ia)}^{2}}}\] \[=\pm \,(b-ia)\]
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