Which one of the following is a square root of -\sqrt{-1}?
- A. 1+i
- B. \frac{1-i}{\sqrt{2}} ✓
- C. \frac{1+i}{\sqrt{2}}
- D. \frac{1}{\sqrt{2}}i
Correct Answer: B. \frac{1-i}{\sqrt{2}}
Explanation
We need to find \sqrt{-i}. Squaring the option \frac{1-i}{\sqrt{2}} yields \frac{(1-i)^2}{2} = \frac{1 - 2i + i^2}{2}. Since i^2 = -1, this evaluates to \frac{-2i}{2} = -i, which is -\sqrt{-1}.
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