Lösung 3.2:5c

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+i)(1−i)  therefore has an argument which is the sum of the argument for the 3+i  and 1−i, i.e.

arg(3+i)(1−i)=arg(3+i)+arg(1−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,

arg(3+i)(1−i)=arg(3+i)+arg(1−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.