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受欢迎的代数 >

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

解答

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

解答

x = \frac{2 + 13}{2} + \frac{3}{2 2 + 13} i, x = - \frac{2 + 13}{2} - \frac{3}{2 2 + 13} i

求解步骤

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

替代

x = a + bi

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

展开

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

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

将

0

改写成标准复数形式:

0 + 0 i

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

[a^{2} - b^{2} - 2 = 0 - 3 + 2 ab = 0] : a = \frac{2 + 13}{2}, a = - \frac{2 + 13}{2}, b = \frac{3}{2 2 + 13} b = - \frac{3}{2 2 + 13}

x = a + bi

代回

x = \frac{2 + 13}{2} + \frac{3}{2 2 + 13} i, x = - \frac{2 + 13}{2} - \frac{3}{2 2 + 13} i

流行的例子

2 x^{2} - 2 i x - 1 = 0

3x+y+(2x+2y)i=13

3 x + y + (2 x + 2 y) i = 13

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\frac{x ^{2} - 5}{2 x + i} = 0

2x+2y=2x+2yi+10

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(x+y)+(x-y)i=2+4i

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