de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

z^4-z^2+1=0

Lösung

z^{4} - z^{2} + 1 = 0

Lösung

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

Schritte zur Lösung

z^{4} - z^{2} + 1 = 0

Schreibe die Gleichung um mit

u = z^{2}

und

u^{2} = z^{4}

u^{2} - u + 1 = 0

Löse

u^{2} - u + 1 = 0 : u = \frac{1}{2} + i \frac{3}{2}, u = \frac{1}{2} - i \frac{3}{2}

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

Setze

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

löse für

z

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

16 x^{4} = 41 x^{2} - 25

x^{3} - 5000000 = 0

x^3-x^2-15x+15=0

x^{3} - x^{2} - 15 x + 15 = 0

x^{3} - x + 10 = 0

4 x^{3} - 256 = 0