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受欢迎的代数 >

z^4+2iz^2+3=0

解答

z^{4} + 2 i z^{2} + 3 = 0

解答

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

求解步骤

z^{4} + 2 i z^{2} + 3 = 0

整理后得

(z^{4} + 3) + 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} + 2 i z^{2} + 3 = 0

用

u = z^{2}

和

u^{2} = z^{4}

改写方程式

u^{2} + 2 i u + 3 = 0

解

u^{2} + 2 i u + 3 = 0 : u = - 3 i, u = i

u = - 3 i, u = i

代回

u = z^{2}

，求解

z

解

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

解

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

解为

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

流行的例子

\frac{1}{2} a = n^{3}

solvefor a,a^3=b^3

so l v e f or a, a^{3} = b^{3}

x^{3} + 5 = 0

solvefor x,x^4-3x^2+2=0

so l v e f or x, x^{4} - 3 x^{2} + 2 = 0

10 = 500 (b)^{3}