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受欢迎的代数 >

x^2-i=0

解答

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

(2+xi)+(y+3i)=7+4i

(2 + x i) + (y + 3 i) = 7 + 4 i

(a + bi)^{2} = 3 + 4 i

∣ z - i ∣ = 1

x^{2} = 4 i

3x+2iy-ix+5y=7+5i

3 x + 2 i y - i x + 5 y = 7 + 5 i