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