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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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1possible duplicate of what is the square root of i?, see also How can you find the complex roots of i? – t.b. Oct 02 '11 at 20:19
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Yes. The two solutions are $z=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i$ and $z=-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i$
hmakholm left over Monica
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