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Beliebt Algebra >

-z^8=-64

Lösung

- z^{8} = - 64

Lösung

z = 4 2^{3}, z = - 4 2^{3}, z = 4 2^{3} i, z = - 4 2^{3} i, z = 42 + 42 i, z = - 42 - 42 i, z = 42 - 42 i, z = - 42 + 42 i

Schritte zur Lösung

- z^{8} = - 64

Teile beide Seiten durch

- 1

z^{8} = 64

Schreibe die Gleichung um mit

u = z^{2}

und

u^{4} = z^{8}

u^{4} = 64

Löse

u^{4} = 64 : u = 22, u = - 22, u = 22 i, u = - 22 i

u = 22, u = - 22, u = 22 i, u = - 22 i

Setze

u = z^{2} w i e d er e in,

löse für

z

Löse

z^{2} = 22 : z = 4 2^{3}, z = - 4 2^{3}

Löse

z^{2} = - 22 : z = 4 2^{3} i, z = - 4 2^{3} i

Löse

z^{2} = 22 i : z = 42 + 42 i, z = - 42 - 42 i

Löse

z^{2} = - 22 i : z = 42 - 42 i, z = - 42 + 42 i

Die Lösungen sind

z = 4 2^{3}, z = - 4 2^{3}, z = 4 2^{3} i, z = - 4 2^{3} i, z = 42 + 42 i, z = - 42 - 42 i, z = 42 - 42 i, z = - 42 + 42 i

Graph

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