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人気のある代数 >

x^5+4+4i=0

解

x^{5} + 4 + 4 i = 0

解

x = \frac{4 + 10 - 2 5}{2} - i \frac{4 - 10 - 2 5}{2}, x = 1 + i, x = - \frac{4 - 10 - 2 5}{2} + i \frac{4 + 10 - 2 5}{2}, x = - \frac{4 + 10 + 2 5}{2} - i \frac{4 - 10 + 2 5}{2}, x = - \frac{4 - 10 + 2 5}{2} - i \frac{4 + 10 + 2 5}{2}

解答ステップ

x^{5} + 4 + 4 i = 0

4 i

を右側に移動します

x^{5} + 4 = - 4 i

4

を右側に移動します

x^{5} = - 4 i - 4

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 = 5, a = - 4 i - 4

∣ a ∣ = 42

ar g (a) = \frac{π}{4} - π

x = 542 (cos (\frac{\frac{π}{4} - π + 2 \cdot 0 π}{5}) + i sin (\frac{\frac{π}{4} - π + 2 \cdot 0 π}{5})), x = 542 (cos (\frac{\frac{π}{4} - π + 2 \cdot 1 π}{5}) + i sin (\frac{\frac{π}{4} - π + 2 \cdot 1 π}{5})), x = 542 (cos (\frac{\frac{π}{4} - π + 2 \cdot 2 π}{5}) + i sin (\frac{\frac{π}{4} - π + 2 \cdot 2 π}{5})), x = 542 (cos (\frac{\frac{π}{4} - π + 2 \cdot 3 π}{5}) + i sin (\frac{\frac{π}{4} - π + 2 \cdot 3 π}{5})), x = 542 (cos (\frac{\frac{π}{4} - π + 2 \cdot 4 π}{5}) + i sin (\frac{\frac{π}{4} - π + 2 \cdot 4 π}{5}))

簡素化

542 (cos (\frac{\frac{π}{4} - π + 2 \cdot 0 π}{5}) + i sin (\frac{\frac{π}{4} - π + 2 \cdot 0 π}{5})) : \frac{4 + 10 - 2 5}{2} - i \frac{4 - 10 - 2 5}{2}

簡素化

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

簡素化

542 (cos (\frac{\frac{π}{4} - π + 2 \cdot 2 π}{5}) + i sin (\frac{\frac{π}{4} - π + 2 \cdot 2 π}{5})) : - \frac{4 - 10 - 2 5}{2} + i \frac{4 + 10 - 2 5}{2}

簡素化

542 (cos (\frac{\frac{π}{4} - π + 2 \cdot 3 π}{5}) + i sin (\frac{\frac{π}{4} - π + 2 \cdot 3 π}{5})) : - \frac{4 + 10 + 2 5}{2} - i \frac{4 - 10 + 2 5}{2}

簡素化

542 (cos (\frac{\frac{π}{4} - π + 2 \cdot 4 π}{5}) + i sin (\frac{\frac{π}{4} - π + 2 \cdot 4 π}{5})) : - \frac{4 - 10 + 2 5}{2} - i \frac{4 + 10 + 2 5}{2}

x = \frac{4 + 10 - 2 5}{2} - i \frac{4 - 10 - 2 5}{2}, x = 1 + i, x = - \frac{4 - 10 - 2 5}{2} + i \frac{4 + 10 - 2 5}{2}, x = - \frac{4 + 10 + 2 5}{2} - i \frac{4 - 10 + 2 5}{2}, x = - \frac{4 - 10 + 2 5}{2} - i \frac{4 + 10 + 2 5}{2}

人気の例

x^{3} - x^{2} = 18

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

3x^4-24x^3+4x^2-29x-67=0

3 x^{4} - 24 x^{3} + 4 x^{2} - 29 x - 67 = 0

roo t s x^{3} + 2 x + 2

x^6-3x^4-x^3+2x^2-x-1=0

x^{6} - 3 x^{4} - x^{3} + 2 x^{2} - x - 1 = 0