Processing Math: Done

Aus Online Mathematik Brückenkurs 2

Powers are repeated multiplications and because multiplication is a relatively simple arithmetical operation when it is carried out in polar form, calculating powers also becomes fairly simple in polar form:

rcos+isinn=rncosn+isinn 

The equation above is called de Moivre's formula.

The plan is therefore to rewrite 1+i in polar form, raised the expression to the power 12 using de Moivre's formula and then to write the answer in the form a+ib.

Using the calculations above, we see that

1+i=2cos4+isin4 

de Moivre's formula now gives

1+i12=212cos124+isin124=22112cos3+isin3=26−1+i0=64−1=−64