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受欢迎的代数 >

solvefor x,x^2+i=0

解答

求解

x, x^{2} + i = 0

解答

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

求解步骤

x^{2} + i = 0

替代

x = a + bi

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

展开

(a + bi)^{2} + i : (a^{2} - b^{2}) + i (1 + 2 ab)

(a^{2} - b^{2}) + i (1 + 2 ab) = 0

将

0

改写成标准复数形式:

0 + 0 i

(a^{2} - b^{2}) + i (1 + 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} = 0 1 + 2 ab = 0]

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

x = a + bi

代回

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

流行的例子

z^2-(5+6i)z+(4+24i)=0

z^{2} - (5 + 6 i) z + (4 + 24 i) = 0

1+2i=(2-i)/(z-1)

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

∣ z + i ∣ = 2

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4 (4 i + 6) = (4 x) i + 8 y

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