Aus Online Mathematik Brückenkurs 2

The argument of a complex number is the angle of the line between the origin and the number measured with respect the positive real number axis.

In this case, we see directly that \displaystyle -10 has the argument \displaystyle \pi.

Note: All angles that correspond to the same direction differ by a whole number of turns, i.e. a multiple of \displaystyle 2\pi, and therefore we could have just as well answered \displaystyle -\pi, \displaystyle 3\pi, \displaystyle 5\pi etc. However, it is usual to give the argument between \displaystyle 0 and \displaystyle 2\pi or between \displaystyle -\pi and \displaystyle \pi.