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受欢迎的代数 >

z^4+iz^2+2=0

解答

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

解答

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

求解步骤

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

整理后得

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

改写成标准形式

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

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

用

u = z^{2}

和

u^{2} = z^{4}

改写方程式

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

解

u^{2} + i u + 2 = 0 : u = - 2 i, u = i

u = - 2 i, u = i

代回

u = z^{2}

，求解

z

解

z^{2} = - 2 i : z = - 1 + i, z = 1 - i

解

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

解为

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

流行的例子

8x^3-52x^2+78x-27=0

8 x^{3} - 52 x^{2} + 78 x - 27 = 0

3 x^{3} + 48 = 0

1/6 a^4=1,a^2=1

\frac{1}{6} a^{4} = 1, a^{2} = 1

4 x^{3} + 8 x = 0

-12x^5-6x^3=-10

- 12 x^{5} - 6 x^{3} = - 10