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受欢迎的代数 >

z^5=4-4sqrt(3)i

解答

z^{5} = 4 - 43 i

解答

z = 58 cos (\frac{π}{15}) - 58 i sin (\frac{π}{15}), z = \frac{5 8}{2} + i \frac{5 8 3}{2}, z = 58 cos (\frac{11 π}{15}) + 58 i sin (\frac{11 π}{15}), z = 58 cos (\frac{17 π}{15}) + 58 i sin (\frac{17 π}{15}), z = 58 cos (\frac{23 π}{15}) + 58 i sin (\frac{23 π}{15})

求解步骤

z^{5} = 4 - 43 i

For

z^{n} = a

the solutions are

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

对于

n = 5, a = 4 - 43 i

∣ a ∣ = 8

ar g (a) = - \frac{π}{3}

z = 58 (cos (\frac{- \frac{π}{3} + 2 \cdot 0 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 0 π}{5})), z = 58 (cos (\frac{- \frac{π}{3} + 2 \cdot 1 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 1 π}{5})), z = 58 (cos (\frac{- \frac{π}{3} + 2 \cdot 2 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 2 π}{5})), z = 58 (cos (\frac{- \frac{π}{3} + 2 \cdot 3 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 3 π}{5})), z = 58 (cos (\frac{- \frac{π}{3} + 2 \cdot 4 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 4 π}{5}))

化简

58 (cos (\frac{- \frac{π}{3} + 2 \cdot 0 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 0 π}{5})) : 58 cos (\frac{π}{15}) - 58 i sin (\frac{π}{15})

化简

58 (cos (\frac{- \frac{π}{3} + 2 \cdot 1 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 1 π}{5})) : \frac{5 8}{2} + i \frac{5 8 3}{2}

化简

58 (cos (\frac{- \frac{π}{3} + 2 \cdot 2 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 2 π}{5})) : 58 cos (\frac{11 π}{15}) + 58 i sin (\frac{11 π}{15})

化简

58 (cos (\frac{- \frac{π}{3} + 2 \cdot 3 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 3 π}{5})) : 58 cos (\frac{17 π}{15}) + 58 i sin (\frac{17 π}{15})

化简

58 (cos (\frac{- \frac{π}{3} + 2 \cdot 4 π}{5}) + i sin (\frac{- \frac{π}{3} + 2 \cdot 4 π}{5})) : 58 cos (\frac{23 π}{15}) + 58 i sin (\frac{23 π}{15})

z = 58 cos (\frac{π}{15}) - 58 i sin (\frac{π}{15}), z = \frac{5 8}{2} + i \frac{5 8 3}{2}, z = 58 cos (\frac{11 π}{15}) + 58 i sin (\frac{11 π}{15}), z = 58 cos (\frac{17 π}{15}) + 58 i sin (\frac{17 π}{15}), z = 58 cos (\frac{23 π}{15}) + 58 i sin (\frac{23 π}{15})

流行的例子

-x^3+18x^2-103x+186=0

- x^{3} + 18 x^{2} - 103 x + 186 = 0

4 x^{3} = 48, x

0=3x^4+4x^3-12x^2+12

0 = 3 x^{4} + 4 x^{3} - 12 x^{2} + 12

15 x^{4} + 7 x^{2} - 2 = 0

x^3-5x^2+3x= 1/2

x^{3} - 5 x^{2} + 3 x = \frac{1}{2}