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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

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  • $\begingroup$ I would write $ x = 1+i, 1-i, -1+i, -1-i$ (with maybe a line break). No need to complicate things. $\endgroup$ – talbi Mar 2 at 10:24
  • $\begingroup$ I don't think that $1\pm i, -1\pm i,$ can be regarded as either ambiguous or confusing. However, while technically, a case could be made that $\pm 1 \pm i$ is similarly unambiguous, some may find it confusing/ambiguous. $\endgroup$ – user2661923 Mar 2 at 10:29
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    $\begingroup$ Overkill: $x\in\{\sqrt{2}e^{i\pi a}\mid a=k+1/4,k\in\mathbb{Z}\}$ $\endgroup$ – Pixel Mar 2 at 10:44
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Do you think $$(-1)^x \left( 1 \pm i \right) \\ x\in\{0,1\}$$ is a nice idea?

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Suggestion: let $z=1+i$ and

$$x \in \{z , \bar z, -z , - \bar z \}.$$

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Another variation is \begin{align*} x^4=-4 \end{align*}

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  • $\begingroup$ The question asked for a method to combine plus and minus. It never came to me that + and - could sum up to zero ;). Now there is no need of sums! $\endgroup$ – SteelCubes Mar 3 at 6:06
  • $\begingroup$ @SteelCubes: Yes, thanks to the fundamental theorem of algebra we can encode the wanted information as precisely the zeros of a polynomial of fourth degree. :-) $\endgroup$ – Markus Scheuer Mar 3 at 6:54
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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.

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  • $\begingroup$ I've used things like $\pm^a(x\pm^b y)$, but only for personal calculations, not public consumption. ;) $\endgroup$ – PM 2Ring Mar 2 at 19:40

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