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受欢迎的代数 >

z^2-3+2i=0,z

解答

z^{2} - 3 + 2 i = 0, z

解答

z = \frac{3 + 13}{2} - \frac{13 - 3}{2} i, z = - \frac{3 + 13}{2} + \frac{13 - 3}{2} i

求解步骤

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

替代

z = x + y i

(x + y i)^{2} - 3 + 2 i = 0

展开

(x + y i)^{2} - 3 + 2 i : (x^{2} - y^{2} - 3) + i (2 + 2 x y)

(x^{2} - y^{2} - 3) + i (2 + 2 x y) = 0

将

0

改写成标准复数形式:

0 + 0 i

(x^{2} - y^{2} - 3) + i (2 + 2 x y) = 0 + 0 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[x^{2} - y^{2} - 3 = 0 2 + 2 x y = 0]

[x^{2} - y^{2} - 3 = 0 2 + 2 x y = 0] : x = \frac{3 + 13}{2}, x = - \frac{3 + 13}{2}, y = - \frac{13 - 3}{2} y = \frac{13 - 3}{2}

z = x + y i

代回

z = \frac{3 + 13}{2} - \frac{13 - 3}{2} i, z = - \frac{3 + 13}{2} + \frac{13 - 3}{2} i

流行的例子

zz = 13 - 13 i

x^{2} + 1 = i

a^2+b^2+a-bi=11+3i

a^{2} + b^{2} + a - bi = 11 + 3 i

solvefor t,a=(Vf-Vi)/t

so l v e f or t, a = \frac{V f - Vi}{t}

\frac{1}{z} = 1 - i