Răspunsuri

2014-11-03T14:01:41+02:00
Sriem sub forma trigonometrica: z=r(\cos\alpha+i\sin\alpha)

Acum, evident ca r=1 .

Atunci avem:  z^4=\cos 4\alpha+i\sin 4\alpha

Iar ecuatia noastra este: \cos 4\alpha+i\sin 4\alpha=i

De unde rezulta:

\cos 4\alpha=0\\ \sin 4\alpha=1

De unde ne dam seama imediat ca:

4\alpha=\frac{\pi}{2}\\ \\ \\ \alpha=\dfrac{\pi}{8}.

Asa ca solutia va fi:

z=\cos\frac{\pi}{8}+i\sin\frac{\pi}{8}