Sriem sub forma trigonometrica: [tex]z=r(\cos\alpha+i\sin\alpha)[/tex]
Acum, evident ca [tex]r=1[/tex] .
Atunci avem: [tex]z^4=\cos 4\alpha+i\sin 4\alpha[/tex]
Iar ecuatia noastra este: [tex]\cos 4\alpha+i\sin 4\alpha=i[/tex]
De unde rezulta:
[tex]\cos 4\alpha=0\\ \sin 4\alpha=1[/tex]
De unde ne dam seama imediat ca:
[tex]4\alpha=\frac{\pi}{2}\\ \\ \\ \alpha=\dfrac{\pi}{8}.[/tex]
Asa ca solutia va fi:
[tex]z=\cos\frac{\pi}{8}+i\sin\frac{\pi}{8}[/tex]
