Solving sqrt(i)=z, one or two solutions?

[Nigel (UK)]

(10-25-2018 04:43 PM)sasa Wrote:  ...
Actually, if we need to "transform" \( \sqrt{i} \), exact alternative would be: (\(-1)^{\frac{1}{4}}\). Alternate form as \(\frac{1+i}{\sqrt{2}}\) is not quite correct - anyone is free to prove differently.

I don't understand why \((1+i)/\sqrt2\) is "not quite correct" as the value of \(\sqrt{i}\). Squaring it does give \(i\), and, assuming that the square root function on the Prime has a cut along the negative real axis in the complex plane, this value is the correct analytic continuation of the square root function defined in the usual way for non-negative real numbers.

Can you explain what the problem is?

Nigel (UK)