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

[sasa]

Albert,

That is exactly the point.

Since here \(\frac{1+i}{\sqrt{2}}\) is just a "principal value", equally good/bad could be \(-\frac{1+i}{\sqrt{2}}\). Furthermore, logical question here is how to choose "principal value"? The answer is: arbitrary.

That is the reason to keep it as is, since evaluating it in an expression with "principal value", we may get result we hardly expect. It is probably not likely to happens in most of practical uses, but it is theoretically possible.