TITLE: How to represent combinations of plus and minus
QUESTION [6 upvotes]: Just wondering if there is a shortcut for representing the following:
$$x=1+i,1-i,-1+i,-1-i$$
I know that you can do:
$$x = 1\pm i,-1\pm i$$
But can you use something like:
$$x = \pm 1 \pm i$$
NOTE: I know the example above just gives $x = 1+i, -1-i$, but I just wanted to provide an example

REPLY [2 votes]: Writing $$x = \pm 1 \pm i$$
is ambiguous as it could either mean $x \in \{1+i,-1-i\}$ or the intended $x \in \{1+i,1-i,-1+i,-1-i\}$. You can make it unambiguous by specifying (in words) that the $\pm$-signs can be chosen independently. I've also seen $x = \pm 1 \pm' i$ to make the independence of the $\pm$-signs explicit in the notation, but I'm not sure that's very common.