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what is the square root of i?

I know that $i^2=-1$, and so $i$ necessarily equals $\sqrt{-1}$. But is it possible to write $i$ as the multiplication of two complex numbers, i.e. can we find a complex number $z$ so that $z^2=i$?

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marked as duplicate by t.b., Zev Chonoles Oct 2 '11 at 20:20

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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possible duplicate of what is the square root of i?, see also How can you find the complex roots of i? –  t.b. Oct 2 '11 at 20:19

1 Answer 1

Yes. The two solutions are $z=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i$ and $z=-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i$

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