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受欢迎的代数 >

z^6=8

解答

z^{6} = 8

解答

z = 2, z = - 2, z = \frac{1}{2} + \frac{3}{2} i, z = - \frac{1}{2} - \frac{3}{2} i, z = \frac{1}{2} - \frac{3}{2} i, z = - \frac{1}{2} + \frac{3}{2} i

求解步骤

z^{6} = 8

用

u = z^{2}

和

u^{3} = z^{6}

改写方程式

u^{3} = 8

解

u^{3} = 8 : u = 38, u = 38 \frac{- 1 + 3 i}{2}, u = 38 \frac{- 1 - 3 i}{2}

u = 38, u = 38 \frac{- 1 + 3 i}{2}, u = 38 \frac{- 1 - 3 i}{2}

代回

u = z^{2}

，求解

z

解

z^{2} = 38 : z = 2, z = - 2

解

z^{2} = 38 \frac{- 1 + 3 i}{2} : z = \frac{1}{2} + \frac{3}{2} i, z = - \frac{1}{2} - \frac{3}{2} i

解

z^{2} = 38 \frac{- 1 - 3 i}{2} : z = \frac{1}{2} - \frac{3}{2} i, z = - \frac{1}{2} + \frac{3}{2} i

解为

z = 2, z = - 2, z = \frac{1}{2} + \frac{3}{2} i, z = - \frac{1}{2} - \frac{3}{2} i, z = \frac{1}{2} - \frac{3}{2} i, z = - \frac{1}{2} + \frac{3}{2} i

作图

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