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人気のある代数 >

ix^6-1=0

解

i x^{6} - 1 = 0

解

x = \frac{2 ( 1 + 3 )}{4} + i \frac{2 ( 1 - 3 )}{4}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2 ( 1 - 3 )}{4} + i \frac{2 ( 1 + 3 )}{4}, x = \frac{2 ( - 1 - 3 )}{4} + i \frac{2 ( - 1 + 3 )}{4}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2 ( - 1 + 3 )}{4} + i \frac{2 ( - 1 - 3 )}{4}

解答ステップ

i x^{6} - 1 = 0

1

を右側に移動します

i x^{6} = 1

以下で両辺を割る

i

x^{6} = - i

z^{n} = a

の場合, 解は

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

以下のため:

n = 6, a = - i

∣ a ∣ = 1

ar g (a) = - \frac{π}{2}

x = 61 (cos (\frac{- \frac{π}{2} + 2 \cdot 0 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 0 π}{6})), x = 61 (cos (\frac{- \frac{π}{2} + 2 \cdot 1 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 1 π}{6})), x = 61 (cos (\frac{- \frac{π}{2} + 2 \cdot 2 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 2 π}{6})), x = 61 (cos (\frac{- \frac{π}{2} + 2 \cdot 3 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 3 π}{6})), x = 61 (cos (\frac{- \frac{π}{2} + 2 \cdot 4 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 4 π}{6})), x = 61 (cos (\frac{- \frac{π}{2} + 2 \cdot 5 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 5 π}{6}))

簡素化

61 (cos (\frac{- \frac{π}{2} + 2 \cdot 0 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 0 π}{6})) : \frac{2 ( 1 + 3 )}{4} + i \frac{2 ( 1 - 3 )}{4}

簡素化

61 (cos (\frac{- \frac{π}{2} + 2 \cdot 1 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 1 π}{6})) : \frac{2}{2} + i \frac{2}{2}

簡素化

61 (cos (\frac{- \frac{π}{2} + 2 \cdot 2 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 2 π}{6})) : \frac{2 ( 1 - 3 )}{4} + i \frac{2 ( 1 + 3 )}{4}

簡素化

61 (cos (\frac{- \frac{π}{2} + 2 \cdot 3 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 3 π}{6})) : \frac{2 ( - 1 - 3 )}{4} + i \frac{2 ( - 1 + 3 )}{4}

簡素化

61 (cos (\frac{- \frac{π}{2} + 2 \cdot 4 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 4 π}{6})) : - \frac{2}{2} - i \frac{2}{2}

簡素化

61 (cos (\frac{- \frac{π}{2} + 2 \cdot 5 π}{6}) + i sin (\frac{- \frac{π}{2} + 2 \cdot 5 π}{6})) : \frac{2 ( - 1 + 3 )}{4} + i \frac{2 ( - 1 - 3 )}{4}

x = \frac{2 ( 1 + 3 )}{4} + i \frac{2 ( 1 - 3 )}{4}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2 ( 1 - 3 )}{4} + i \frac{2 ( 1 + 3 )}{4}, x = \frac{2 ( - 1 - 3 )}{4} + i \frac{2 ( - 1 + 3 )}{4}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2 ( - 1 + 3 )}{4} + i \frac{2 ( - 1 - 3 )}{4}

人気の例

w^{3} - 2 w^{2} + w = 2

x^{6} + 7 2^{3} + 512 = 0

k^{3} = 8

x^4+x^3+x^2+x^1=1

x^{4} + x^{3} + x^{2} + x^{1} = 1

(17x-11)^3-(17x-11)=0

(17 x - 11)^{3} - (17 x - 11) = 0