# Can i be written as the multiplication of two complex numbers? [duplicate]

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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## marked as duplicate by t.b., Zev ChonolesOct 2 '11 at 20:20

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