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Beliebt Algebra >

x^4-64i=0

Lösung

x^{4} - 64 i = 0

Lösung

x = 4 + 22 + i 4 - 22, x = - 4 - 22 + i 4 + 22, x = - 4 + 22 - i 4 - 22, x = 4 - 22 - i 4 + 22

Schritte zur Lösung

x^{4} - 64 i = 0

Verschiebe

64 i

auf die rechte Seite

x^{4} = 64 i

Für

z^{n} = a

sind die Lösungen

z_{k} = n ∣ a ∣ (cos (\frac{ar g ( a ) + 2 kπ}{n}) + i sin (\frac{ar g ( a ) + 2 kπ}{n})),

k = 0, 1, \dots, n - 1

Für

n = 4, a = 64 i

∣ a ∣ = 64

ar g (a) = \frac{π}{2}

x = 464 (cos (\frac{\frac{π}{2} + 2 \cdot 0 π}{4}) + i sin (\frac{\frac{π}{2} + 2 \cdot 0 π}{4})), x = 464 (cos (\frac{\frac{π}{2} + 2 \cdot 1 π}{4}) + i sin (\frac{\frac{π}{2} + 2 \cdot 1 π}{4})), x = 464 (cos (\frac{\frac{π}{2} + 2 \cdot 2 π}{4}) + i sin (\frac{\frac{π}{2} + 2 \cdot 2 π}{4})), x = 464 (cos (\frac{\frac{π}{2} + 2 \cdot 3 π}{4}) + i sin (\frac{\frac{π}{2} + 2 \cdot 3 π}{4}))

Vereinfache

464 (cos (\frac{\frac{π}{2} + 2 \cdot 0 π}{4}) + i sin (\frac{\frac{π}{2} + 2 \cdot 0 π}{4})) : 4 + 22 + i 4 - 22

Vereinfache

464 (cos (\frac{\frac{π}{2} + 2 \cdot 1 π}{4}) + i sin (\frac{\frac{π}{2} + 2 \cdot 1 π}{4})) : - 4 - 22 + i 4 + 22

Vereinfache

464 (cos (\frac{\frac{π}{2} + 2 \cdot 2 π}{4}) + i sin (\frac{\frac{π}{2} + 2 \cdot 2 π}{4})) : - 4 + 22 - i 4 - 22

Vereinfache

464 (cos (\frac{\frac{π}{2} + 2 \cdot 3 π}{4}) + i sin (\frac{\frac{π}{2} + 2 \cdot 3 π}{4})) : 4 - 22 - i 4 + 22

x = 4 + 22 + i 4 - 22, x = - 4 - 22 + i 4 + 22, x = - 4 + 22 - i 4 - 22, x = 4 - 22 - i 4 + 22

Beliebte Beispiele

0=9x^5+72x^2+4x^4+32x

0 = 9 x^{5} + 72 x^{2} + 4 x^{4} + 32 x

x^3-300x-3000=0

x^{3} - 300 x - 3000 = 0

9 + 5 x^{2} = 4 x^{4}

m^{3} - 64 m = 0

- x^{4} - x^{2} + 8 = 0