Lösung 3.2:6f

Aus Online Mathematik Brückenkurs 2

We can write every factor in the numerator and denominator in polar form and then use the arithmetical rules for multiplication and division in polar form:

r1cos+isinr2cos+isin=r1r2r2cos+isinr1cos+isin=r2r1cos−+isin−

In fact, most of the work consists of writing all the factors in polar form:

The whole expression becomes

3i12−2i2+2i1+i3=22cos4+isin42cos3+isin33cos2+isin24cos−6+isin−6=12cos2−6+isin2−642cos4+3+isin4+3=12cos3+isin342cos712+isin712=1242cos127−3+isin127−3=32cos4+isin4