A) (a) \[i\sqrt{2}\]
B) (b) \[\frac{i}{i\sqrt{2}}\]
C) (c) 0
D) (d) \[-i\sqrt{2}\]
Correct Answer: A
Solution :
[a] \[\because i=0+1\] \[=\frac{1}{2}\left( 0+2i \right)=\frac{1}{2}{{\left( 1-i \right)}^{2}}\] \[\therefore \sqrt{i}=\pm \frac{1}{\sqrt{2}}(1+i)\]Taking positive sign, we have \[\sqrt{-i}=\frac{1}{\sqrt{2}}(1+i)\And \sqrt{i}-\sqrt{-i}=\frac{1}{\sqrt{2}}(1+i-1+i)\] \[=\frac{2i}{\sqrt{2}}=\sqrt{2}i\]Hence, option [a] is correct.
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