Square roots of -i, where i = sqrt - 1 , are

cos( - 4 ) + isin ( - 4 ),cos ( 3 4 ) + isin ( 3 4 )

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Complex Variable

Square roots of -i, where $${\text{i}} = \sqrt { - 1} ,$$ are

A) $${\text{i}},\, - {\text{i}}$$ B) $${\text{cos}}\left( { - \frac{\pi }{4}} \right) + {\text{i}}\sin \left( { - \frac{\pi }{4}} \right),\,\cos \left( {\frac{{3\pi }}{4}} \right) + {\text{i}}\sin \left( {\frac{{3\pi }}{4}} \right)$$ C) $${\text{cos}}\left( {\frac{\pi }{4}} \right) + {\text{i}}\sin \left( {\frac{{3\pi }}{4}} \right),\,\cos \left( {\frac{{3\pi }}{4}} \right) + {\text{i}}\sin \left( {\frac{\pi }{4}} \right)$$ D) $${\text{cos}}\left( {\frac{{3\pi }}{4}} \right) + {\text{i}}\sin \left( { - \frac{{3\pi }}{4}} \right),\,\cos \left( { - \frac{{3\pi }}{4}} \right) + {\text{i}}\sin \left( {\frac{{3\pi }}{4}} \right)$$

Answer & Solution

Correct Answer: Option B

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Square roots of -i, where $${\text{i}} = \sqrt { - 1} ,$$ are

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