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Possible Duplicate:
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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    possible duplicate of [what is the square root of i?](http://math.stackexchange.com/questions/3315/what-is-the-square-root-of-i), see also [How can you find the complex roots of i?](http://math.stackexchange.com/questions/5747/how-can-you-find-the-complex-roots-of-i)2011-10-02

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