I was doing some complex numbers problems today and something has me really confused. I had to find the arument of -2-2root3i so I plotted the point on an argand diagram and used tan to find the reference angle. Then I added pi to it because thats what the book said to do for the 3rd quadrant in the previous questions and because I thought the argument was the angle between the positive x axis and the line joining the complex number to the origin. I always that it was in an anticlockwise direction. But this time the book said to add -pi and continued to do this for the rest of the questions. Now i am confused as to how i find the argument. Can someone please help.

Thanks