Complex numbers: Argument of Z help

I'm having some problems with finding, in radians, the argument of z and adding rotations of 180 to keep it in range. I know that I have to use:

$\displaystyle tan=\frac{y}{x}$

and I know exact trigonometric ratios, and the ASTC in the polar plane. But I don't know where Arg Z is positive, and I don't know when to add $\displaystyle 2\pi$ or even just $\displaystyle \pi$ (pi = 180 in radians), to keep Arg Z in the range of $\displaystyle -\pi < 0 <\pi$. As you can see I am very confused, any help would be great.