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Beliebt Algebra >

x^6=32sqrt(3)+32i

Lösung

x^{6} = 323 + 32 i

Lösung

x = 2 cos (\frac{π}{36}) + 2 i sin (\frac{π}{36}), x = 2 cos (\frac{13 π}{36}) + 2 i sin (\frac{13 π}{36}), x = 2 cos (\frac{25 π}{36}) + 2 i sin (\frac{25 π}{36}), x = 2 cos (\frac{37 π}{36}) + 2 i sin (\frac{37 π}{36}), x = 2 cos (\frac{49 π}{36}) + 2 i sin (\frac{49 π}{36}), x = 2 cos (\frac{61 π}{36}) + 2 i sin (\frac{61 π}{36})

Schritte zur Lösung

x^{6} = 323 + 32 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 = 6, a = 323 + 32 i

∣ a ∣ = 64

ar g (a) = \frac{π}{6}

x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 0 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 0 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 1 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 1 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 2 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 2 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 3 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 3 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 4 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 4 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}))

Vereinfache

664 (cos (\frac{\frac{π}{6} + 2 \cdot 0 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 0 π}{6})) : 2 cos (\frac{π}{36}) + 2 i sin (\frac{π}{36})

Vereinfache

664 (cos (\frac{\frac{π}{6} + 2 \cdot 1 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 1 π}{6})) : 2 cos (\frac{13 π}{36}) + 2 i sin (\frac{13 π}{36})

Vereinfache

664 (cos (\frac{\frac{π}{6} + 2 \cdot 2 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 2 π}{6})) : 2 cos (\frac{25 π}{36}) + 2 i sin (\frac{25 π}{36})

Vereinfache

664 (cos (\frac{\frac{π}{6} + 2 \cdot 3 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 3 π}{6})) : 2 cos (\frac{37 π}{36}) + 2 i sin (\frac{37 π}{36})

Vereinfache

664 (cos (\frac{\frac{π}{6} + 2 \cdot 4 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 4 π}{6})) : 2 cos (\frac{49 π}{36}) + 2 i sin (\frac{49 π}{36})

Vereinfache

664 (cos (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 5 π}{6})) : 2 cos (\frac{61 π}{36}) + 2 i sin (\frac{61 π}{36})

x = 2 cos (\frac{π}{36}) + 2 i sin (\frac{π}{36}), x = 2 cos (\frac{13 π}{36}) + 2 i sin (\frac{13 π}{36}), x = 2 cos (\frac{25 π}{36}) + 2 i sin (\frac{25 π}{36}), x = 2 cos (\frac{37 π}{36}) + 2 i sin (\frac{37 π}{36}), x = 2 cos (\frac{49 π}{36}) + 2 i sin (\frac{49 π}{36}), x = 2 cos (\frac{61 π}{36}) + 2 i sin (\frac{61 π}{36})

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