Question about using the notation "$\pm$" to represent the answer briefly. I saw this problem in the book with answer:

Solve the equation $z^4+z^2+1=0$.

The book gave the final answer as:
$$z_1=\frac{1}{2}+ \frac{\sqrt{3}}{2}i, \quad
z_2=\frac{-1}{2}- \frac{\sqrt{3}}{2}i,\quad
z_3=\frac{-1}{2}+ \frac{\sqrt{3}}{2}i,\quad
z_4=\frac{1}{2}- \frac{\sqrt{3}}{2}i.$$
My question isn't about how to solve the equation, But I want to know  Is it possible to write the roots of the equation briefly like: $$z=\pm \frac{1}{2}\pm \frac{\sqrt{3}}{2}i. $$
And does it represent the same $z_1$ , $z_2$ , $z_3$ , $z_4$ I mentioned earlier? And finally I want to know whether this is a common way to represent four answers or not.

You can do that, but you have to be careful. Sometimes $z=\pm \frac{1}{2}\pm \frac{\sqrt{3}}{2}$ will mean the four roots you've mentioned. But sometimes it might mean just the two roots $z_1,z_2$ where the sign is the same, with the other two denoted as $z=\pm \frac{1}{2}\mp \frac{\sqrt{3}}{2}$.
I would probably write what you've written, but add a few clarifying words ("the four roots $z=\pm \frac{1}{2}\pm \frac{\sqrt{3}}{2}$") to make sure there's absolutely no confusion.
