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Aus Online Mathematik Brückenkurs 2

Geometrically, the multiplication of two complex numbers means that there magnitudes are multiplied and their arguments are added. The product 3+i1−i  therefore has an argument which is the sum of the argument for the 3+i  and 1−i, i.e.

arg3+i1−i=arg3+i+arg1−i 

By drawing the factors in the complex plane, we can determine relatively easily the argument using simple trigonometry:

(Because 1−i lies in the fourth quadrant, the argument equals − and not .)

Hence,

arg3+i1−i=arg3+i+arg1−i=6−4=−12 

NOTE: if you prefer to give the argument between 0 and 2, then the answer is

−12+2=12−+24=1223