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Lösung 3.2:5d

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When dividing two complex numbers, the numerator's magnitude is divided by the denominator's magnitude and the numerator's argument is subtracted from the numerator's argument.

The argument of the quotient i(1+i) is therefore

argi1+i=argi−arg(1+i).

We obtain the argument of i and 1+i by drawing the numbers in the complex plane and using a little trigonometry.

Hence, we obtain

argi1+i=argi−arg(1+i)=2−4=4.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.2:5d“