3x^2+6ix=0

解答

3 x^{2} + 6 i x = 0

x = - 2 i, x = 0

求解步骤

3 x^{2} + 6 i x = 0

替代

x = a + bi

3 (a + bi)^{2} + 6 i (a + bi) = 0

展开

3 (a + bi)^{2} + 6 i (a + bi) : (3 a^{2} - 3 b^{2} - 6 b) + i (6 a + 6 ab)

(3 a^{2} - 3 b^{2} - 6 b) + i (6 a + 6 ab) = 0

将

0

改写成标准复数形式:

0 + 0 i

(3 a^{2} - 3 b^{2} - 6 b) + i (6 a + 6 ab) = 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:

[3 a^{2} - 3 b^{2} - 6 b = 0 6 a + 6 ab = 0]

[3 a^{2} - 3 b^{2} - 6 b = 0 6 a + 6 ab = 0] : (a = 0, a = 0, b = - 2 b = 0)

x = a + bi

代回

x = - 2 i, x = 0

- 4 i = \frac{1}{( 1000 \cdot x ) i}

i = - 24 t^{2} + 333 t - 32

(5 - \frac{1}{2} x) + (y - 1) i = 7 - 2 i

(x + 2 i y)^{2} - 8 i + 15 = 0

x = \frac{y}{( 1 + i \cdot n )}