TITLE: How does $\arctan(0)$ equal $\pi?$
QUESTION [14 upvotes]: I was recently doing a problem, and apparently got it wrong. 
The question asked: what is the polar form of the sum: $(5+3i)$ + $(-10-3i)$.
From my understanding, the sum would equal: $-5+0i$
Now,
the magnitude would equal: $\sqrt{-5^2 + 0^2} = 5$
And,
the angle would equal: $\tan^{-1}(\frac{0}{-5}) = 0$
Instead, the answer is actually $5 (\pi)$, instead of $5 (0)$.
I check on this website: 2pif.com (under the "Complex Numbers" tool), and it also says that  5 (0) is the answer.
So I'm wondering, how in the world does $\tan^{-1}(\frac{0}{-5}) = \pi$

REPLY [5 votes]: To add to the other answers here, the argument is the angle the corresponding vector on the Complex Plane would make with that of $1+0i$

In this particular case, the angle is $180^{\circ}$ or $\pi$ radians as in the picture.