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受欢迎的代数 >

z^4=-1+sqrt(3)i

解答

z^{4} = - 1 + 3 i

解答

z = \frac{4 2 3}{2} + i \frac{4 2}{2}, z = - \frac{4 2}{2} + i \frac{4 2 3}{2}, z = - \frac{4 2 3}{2} - i \frac{4 2}{2}, z = \frac{4 2}{2} - i \frac{4 2 3}{2}

求解步骤

z^{4} = - 1 + 3 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 = 4, a = - 1 + 3 i

∣ a ∣ = 2

ar g (a) = - \frac{π}{3} + π

z = 42 (cos (\frac{- \frac{π}{3} + π + 2 \cdot 0 π}{4}) + i sin (\frac{- \frac{π}{3} + π + 2 \cdot 0 π}{4})), z = 42 (cos (\frac{- \frac{π}{3} + π + 2 \cdot 1 π}{4}) + i sin (\frac{- \frac{π}{3} + π + 2 \cdot 1 π}{4})), z = 42 (cos (\frac{- \frac{π}{3} + π + 2 \cdot 2 π}{4}) + i sin (\frac{- \frac{π}{3} + π + 2 \cdot 2 π}{4})), z = 42 (cos (\frac{- \frac{π}{3} + π + 2 \cdot 3 π}{4}) + i sin (\frac{- \frac{π}{3} + π + 2 \cdot 3 π}{4}))

化简

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

化简

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

化简

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

化简

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

z = \frac{4 2 3}{2} + i \frac{4 2}{2}, z = - \frac{4 2}{2} + i \frac{4 2 3}{2}, z = - \frac{4 2 3}{2} - i \frac{4 2}{2}, z = \frac{4 2}{2} - i \frac{4 2 3}{2}

流行的例子

x=-1.3x^3-4x^2-13x-6

x = - 1.3 x^{3} - 4 x^{2} - 13 x - 6

(\frac{1}{5}) x^{5} = 1

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2x-712-4-x^6=1920

2 x - 712 - 4 - x^{6} = 1920

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