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受欢迎的代数 >

z^4+2-2sqrt(3)i=0

解答

z^{4} + 2 - 23 i = 0

解答

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

求解步骤

z^{4} + 2 - 23 i = 0

将

23 i

到右边

z^{4} + 2 = 23 i

将

2

到右边

z^{4} = 23 i - 2

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 = 23 i - 2

∣ a ∣ = 4

ar g (a) = - \frac{π}{3} + π

z = 44 (cos (\frac{- \frac{π}{3} + π + 2 \cdot 0 π}{4}) + i sin (\frac{- \frac{π}{3} + π + 2 \cdot 0 π}{4})), z = 44 (cos (\frac{- \frac{π}{3} + π + 2 \cdot 1 π}{4}) + i sin (\frac{- \frac{π}{3} + π + 2 \cdot 1 π}{4})), z = 44 (cos (\frac{- \frac{π}{3} + π + 2 \cdot 2 π}{4}) + i sin (\frac{- \frac{π}{3} + π + 2 \cdot 2 π}{4})), z = 44 (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

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

化简

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

化简

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

化简

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

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

流行的例子

0=t^3-6t^2+9t+5

0 = t^{3} - 6 t^{2} + 9 t + 5

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

2 x^{4} - 16 x = 0

36 - 12 x - 4 x^{3} = 0

(x - 3)^{3} + 18 = 530