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Lösung 3.2:5c

Aus Online Mathematik Brückenkurs 2

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Version vom 10:39, 11. Mär. 2009

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.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.2:5c“