I am typing up some results in Latex, and I am tempted to include a $\sqrt{-i}$ in the publication. However, this seems ugle to me. How should it appear? Perhaps as $i\sqrt{i}$?
This is purely a style issue, I think. Edit: This is not a style issue see the answer.
How to display $\sqrt{-i}$ (square root of a negative imaginary) in publication?
It depends a lot on the context. First, it is worth noting that the element $-i\in\Bbb{C}$ has two distinct square roots in $\Bbb{C}$, so the expression $\sqrt{-i}$ does not uniquely define a complex number. So before using any symbol at all, I would suggest to define either $$\sqrt{-i}:=\tfrac{1}{\sqrt{2}}+\tfrac{1}{\sqrt{2}}i \qquad\text{ or }\qquad \sqrt{-i}:=\tfrac{1}{\sqrt{2}}-\tfrac{1}{\sqrt{2}}i.$$ Then you can use whatever symbol you prefer; instead of $\sqrt{-i}$ you could use $i\sqrt{i}$ or $i^{\tfrac32}$ or $i^{3/2}$ or more concisely $\alpha$ or $\beta$ or $\gamma$, take your pick.