I’m trying to take a fourth root as an exercise in a complex analysis book. The basic characteristic of a fourth root (I think) is that there is one pair of solutions +/- a, and another pair of solutions +/- a*i. I would much rather have to only write a out once, like +/-(i?) * a.
I’m looking for a compact notation similar to the +/- sign, which would express that there is one solution where the symbol represents the annotated value (in this case i), and another solution where the symbol represents the field’s identity value. Maybe something from category theory?
In the end, I explicitly defined a symbol to represent the set {1, i}. I used the letter k, because I figured j might be too easily confused with i. The set can also be written as k = +sqrt(+/-1).