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受欢迎的代数 >

x^2+x+sqrt(3)i=0

解答

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

解答

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

求解步骤

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

替代

x = a + bi

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

展开

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

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

将

0

改写成标准复数形式:

0 + 0 i

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

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

[a^{2} - b^{2} + a = 0 3 + b + 2 ab = 0] : (a = \frac{1}{2}, a = - \frac{3}{2}, b = - \frac{3}{2} b = \frac{3}{2})

x = a + bi

代回

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

流行的例子

\frac{1}{0} = a + bi

(x^2-2x-15)+(3y-9)i=3i

(x^{2} - 2 x - 15) + (3 y - 9) i = 3 i

3ai-b-3i=a-5+bi

3 ai - b - 3 i = a - 5 + bi

∣ z - 1 + 3 i ∣ = 2

∣ x + bi + 1 + i ∣ = 1