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Beliebt Algebra >

z^8=256

Lösung

z^{8} = 256

Lösung

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

Schritte zur Lösung

z^{8} = 256

Schreibe die Gleichung um mit

u = z^{2}

und

u^{4} = z^{8}

u^{4} = 256

Löse

u^{4} = 256 : u = 4, u = - 4, u = 4 i, u = - 4 i

u = 4, u = - 4, u = 4 i, u = - 4 i

Setze

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

löse für

z

Löse

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

Löse

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

Löse

z^{2} = 4 i : z = 2 + 2 i, z = - 2 - 2 i

Löse

z^{2} = - 4 i : z = 2 - 2 i, z = - 2 + 2 i

Die Lösungen sind

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

Graph

Beliebte Beispiele

m^{4} + m^{2} + 1 = 0

solvefor a,a^3-b^3=0

so l v e f or a, a^{3} - b^{3} = 0

(2x^2-7x)^2+2x^2-7x=20

(2 x^{2} - 7 x)^{2} + 2 x^{2} - 7 x = 20

(x)^3+(3x)^2-x-3=0

(x)^{3} + (3 x)^{2} - x - 3 = 0

(x^2+x+1)^2=x^4+8x^2+1

(x^{2} + x + 1)^{2} = x^{4} + 8 x^{2} + 1