Help with complex numbers?

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

Re: Can someone help me with complex numbers?

The "standard" argument for complex numbers lies between 0 and while "arctan" always gives a value between and . In the case of we are looking at which is ih the first quadrant so we add to get .

**However**, the "argument" of a complex number is not "uniquely" defined. Adding or subtracting to the argument will give another that is also a valid argument for that same complex number. Subtracting from , of course, gives the same as subtracting from . As I said before the "standard" is between 0 and but there might be good reason to use another representation.

Re: Can someone help me with complex numbers?

Thanks so much for your answer! It definitely makes more sense now