What is the principal argument of $-5-5i$? When i calculated it by $\tan^{-1}\dfrac{y}{x}$, I got $\dfrac{\pi}{4}$, then i added $\pi$ to make it in the right quadrant, so my final answer is $\dfrac{5\pi}{4}$
However, the correct answer is $-\dfrac{3\pi}{4}$...why is that?

Using the definition of atan2, $$\arg(-5-5i)=\arctan\left(\frac{-5}{-5}\right)-\pi=\arctan1-\pi=\frac\pi4-\pi$$
