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Beliebt Algebra >

z^6=8

Lösung

z^{6} = 8

Lösung

z = 2, z = - 2, z = \frac{1}{2} + \frac{3}{2} i, z = - \frac{1}{2} - \frac{3}{2} i, z = \frac{1}{2} - \frac{3}{2} i, z = - \frac{1}{2} + \frac{3}{2} i

Schritte zur Lösung

z^{6} = 8

Schreibe die Gleichung um mit

u = z^{2}

und

u^{3} = z^{6}

u^{3} = 8

Löse

u^{3} = 8 : u = 38, u = 38 \frac{- 1 + 3 i}{2}, u = 38 \frac{- 1 - 3 i}{2}

u = 38, u = 38 \frac{- 1 + 3 i}{2}, u = 38 \frac{- 1 - 3 i}{2}

Setze

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

löse für

z

Löse

z^{2} = 38 : z = 2, z = - 2

Löse

z^{2} = 38 \frac{- 1 + 3 i}{2} : z = \frac{1}{2} + \frac{3}{2} i, z = - \frac{1}{2} - \frac{3}{2} i

Löse

z^{2} = 38 \frac{- 1 - 3 i}{2} : z = \frac{1}{2} - \frac{3}{2} i, z = - \frac{1}{2} + \frac{3}{2} i

Die Lösungen sind

z = 2, z = - 2, z = \frac{1}{2} + \frac{3}{2} i, z = - \frac{1}{2} - \frac{3}{2} i, z = \frac{1}{2} - \frac{3}{2} i, z = - \frac{1}{2} + \frac{3}{2} i

Graph

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