Processing Math: Done

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:

• r1(cos+isin)r2(cos+isin)=r1r2cos(+)+isin(+) 

• r2(cos+isin)r1(cos+isin)=r2r1cos(−)+isin(−). 

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

The whole expression becomes

3i(12−2i)(2+2i)(1+i3)=22cos4+isin42cos3+isin33cos2+isin24cos−6+isin−6=12cos2−6+isin2−642cos4+3+isin4+3=12cos3+isin342cos127+isin127=1242cos127−3+isin127−3=32cos4+isin4.