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受欢迎的代数 >

根 z^2+2z-isqrt(3)

解答

根

z^{2} + 2 z - i 3

解答

z = \frac{6 - 2}{2} + \frac{1}{2} i, z = - \frac{6 + 2}{2} - \frac{1}{2} i

求解步骤

z^{2} + 2 z - i 3

根与 X 轴相交

(y = 0)

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

替代

z = x + y i

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

展开

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

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

将

0

改写成标准复数形式:

0 + 0 i

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

[x^{2} - y^{2} + 2 x = 0 - 3 + 2 y + 2 x y = 0] : (x = \frac{6 - 2}{2}, x = - \frac{6 + 2}{2}, y = \frac{1}{2} y = - \frac{1}{2})

z = x + y i

代回

z = \frac{6 - 2}{2} + \frac{1}{2} i, z = - \frac{6 + 2}{2} - \frac{1}{2} i

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