I was looking for a complex extension of the surreals and then I found $\operatorname{No}[i]$, what are its properties and how do I express $x+yi$ in the $a | b$ notation?



What are the properties of $\operatorname{No}[i]$?
The surreal complex field $\text{No}[i]$, known as the [surcomplex field](https://en.wikipedia.org/wiki/Surreal_number#Surcomplex_numbers), is a proper-class-sized set-saturated algebraically closed field. It is universal for all fields of characteristic 0. Indeed, under global choice, every class field structure in characteristic 0 embeds as a subfield of $\text{No}[i]$. It is the algebraic closure of the transcendental field extension of $\mathbb{Q}$ by a proper class of algebraically independent transcendentals.


