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Beliebt Algebra >

z^8=81^2

Lösung

z^{8} = 8 1^{2}

Lösung

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

Schritte zur Lösung

z^{8} = 8 1^{2}

8 1^{2} = 6561

z^{8} = 6561

Schreibe die Gleichung um mit

u = z^{2}

und

u^{4} = z^{8}

u^{4} = 6561

Löse

u^{4} = 6561 : u = 9, u = - 9, u = 9 i, u = - 9 i

u = 9, u = - 9, u = 9 i, u = - 9 i

Setze

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

löse für

z

Löse

z^{2} = 9 : z = 3, z = - 3

Löse

z^{2} = - 9 : z = 3 i, z = - 3 i

Löse

z^{2} = 9 i : z = \frac{3}{2} + \frac{3}{2} i, z = - \frac{3}{2} - \frac{3}{2} i

Löse

z^{2} = - 9 i : z = \frac{3}{2} - \frac{3}{2} i, z = - \frac{3}{2} + \frac{3}{2} i

Die Lösungen sind

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

Graph

Beliebte Beispiele

(n - 2)^{3} = 512

32 t - 2 t^{3} = 0

-5x^3+11x^2-4x-2=0

- 5 x^{3} + 11 x^{2} - 4 x - 2 = 0

solvefor x,x^3-3x^3y=0

so l v e f or x, x^{3} - 3 x^{3} y = 0

x^3+x^2-13x-21=0

x^{3} + x^{2} - 13 x - 21 = 0