Lösung 3.3:1d

Aus Online Mathematik Brückenkurs 2

Because we are going to raise something to the power 12, the base in the expression should be written in polar form. In turn, the base consists of a quotient which it is advantageous to calculate in polar form. Thus, it seems appropriate to write 1+i3  and 1+i in polar form right from the beginning and to carry out all calculations in polar form.

We obtain

1+i3=2cos3+isin31+i=2cos4+isin4 

and

1+i1+i3=2cos3+isin32cos4+isin4=22cos3−4+isin3−4=2cos12+isin12

Finally, de Moivre's formula gives

1+i1+i312=212cos1212+isin1212=22112cos+isin=26−1+i0=−64