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Q. A value of $ \sqrt{i}+\sqrt{-i} $ is

Rajasthan PETRajasthan PET 2011

Solution:

$ \sqrt{i}+\sqrt{-i}=\frac{1}{\sqrt{2}}(\sqrt{2i}+\sqrt{-2i}) $
$ =\frac{1}{2}\{\sqrt{{{(1+i)}^{2}}}+\sqrt{{{(1-i)}^{2}}}\} $
$ =\frac{1}{\sqrt{2}}\{(1+i)+(1+i)\} $
$ =\sqrt{2} $