zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

z^4+4iz^2+8=0

解答

z^{4} + 4 i z^{2} + 8 = 0

解答

z = - \frac{1 + 3}{4 4 + 2 3} + 4 4 + 23 i, z = \frac{1 + 3}{4 4 + 2 3} - 4 4 + 23 i, z = \frac{- 1 + 3}{4 4 - 2 3} + 4 4 - 23 i, z = - \frac{- 1 + 3}{4 4 - 2 3} - 4 4 - 23 i

求解步骤

z^{4} + 4 i z^{2} + 8 = 0

整理后得

(z^{4} + 8) + 4 i z^{2} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

z^{4} + 4 i z^{2} + 8 = 0

用

u = z^{2}

和

u^{2} = z^{4}

改写方程式

u^{2} + 4 i u + 8 = 0

解

u^{2} + 4 i u + 8 = 0 : u = - 2 (1 + 3) i, u = 2 (3 - 1) i

u = - 2 (1 + 3) i, u = 2 (3 - 1) i

代回

u = z^{2}

，求解

z

解

z^{2} = - 2 (1 + 3) i : z = - \frac{1 + 3}{4 4 + 2 3} + 4 4 + 23 i, z = \frac{1 + 3}{4 4 + 2 3} - 4 4 + 23 i

解

z^{2} = 2 (3 - 1) i : z = \frac{- 1 + 3}{4 4 - 2 3} + 4 4 - 23 i, z = - \frac{- 1 + 3}{4 4 - 2 3} - 4 4 - 23 i

解为

z = - \frac{1 + 3}{4 4 + 2 3} + 4 4 + 23 i, z = \frac{1 + 3}{4 4 + 2 3} - 4 4 + 23 i, z = \frac{- 1 + 3}{4 4 - 2 3} + 4 4 - 23 i, z = - \frac{- 1 + 3}{4 4 - 2 3} - 4 4 - 23 i

流行的例子

x^{100} = 0

x^{5} = 4

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

5x^4-15=1-25x-110

5 x^{4} - 15 = 1 - 25 x - 110

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