Trigonometry question using complex numbers on the complex plane

Question

I am not quite sure what this is asking, I tried to square these numbers and then convert into radians but it was not right. I am only used to graphing the absolute value of complex numbers.

Let $z=−5−5\sqrt{3i}$

1. When z is graphed in the complex plane, what radian angle does it make with the positive $x$-axis?
2. What radian angles do $z^2$, $z^3$, and $z^4$ make with the positive $x$-axis? You may want to use your calculator to compute the powers of $z$.
3. For what values of $n$ does $z^n$ lie on the positive x-axis?

Answer 1

$$\arg(-5-5\sqrt3\,i)=\arctan\frac{-5\sqrt3}{-5}=\arctan\sqrt3=\frac\pi3\pm k\pi\;,\;\;k\in\Bbb Z$$

Since $\;-5-5\sqrt3\,i\;$ is in the third quadrant, it must be its argument is $\;\dfrac\pi3+\pi=\dfrac{4\pi}3\;$ (of course, this is defined only up to multiples of $\;2\pi i\;$ )