In my book when converting $.4-.2j$ into polar notation they give the answer: $.45e^{j26.6}$; however, $\arctan(\frac{-.2}{.4}) = -26.6$ according to my calculator.
Can someone attempt to thoroughly explain this to me? I would think that since $.4-.2j$ is in the fourth quadrant then it would have two angles not over $360$ that can represent it: $-26.6$ and $334$. Do you have to flip the sign of any angles outside the range $(\frac{\pi}{2},\frac{-\pi}{2}$)?
Recall that the principal value for the argument $\operatorname{Arg}(z)$ is defined in the interval $(-\pi,\pi]$, therefore since $0.4-0.2j$ lies in the fourth quadrant, its polar form should be $re^{i\theta}$ with $\theta \in (-\pi/2,0)$.