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Beliebt Algebra >

z^8=16

Lösung

z^{8} = 16

Lösung

z = 2, z = - 2, z = 2 i, z = - 2 i, z = 1 + i, z = - 1 - i, z = 1 - i, z = - 1 + i

Schritte zur Lösung

z^{8} = 16

Schreibe die Gleichung um mit

u = z^{2}

und

u^{4} = z^{8}

u^{4} = 16

Löse

u^{4} = 16 : u = 2, u = - 2, u = 2 i, u = - 2 i

u = 2, u = - 2, u = 2 i, u = - 2 i

Setze

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

löse für

z

Löse

z^{2} = 2 : z = 2, z = - 2

Löse

z^{2} = - 2 : z = 2 i, z = - 2 i

Löse

z^{2} = 2 i : z = 1 + i, z = - 1 - i

Löse

z^{2} = - 2 i : z = 1 - i, z = - 1 + i

Die Lösungen sind

z = 2, z = - 2, z = 2 i, z = - 2 i, z = 1 + i, z = - 1 - i, z = 1 - i, z = - 1 + i

Graph

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