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受欢迎的代数 >

(3+2i)x^2+10x+2=0

解答

(3 + 2 i) x^{2} + 10 x + 2 = 0

解答

x = - 0.21265 \dots - \frac{- 0.85061 \dots + 0.83297 \dots}{6} i, x = - 2.09503 \dots + \frac{8.38015 \dots + 0.83297 \dots}{6} i

求解步骤

(3 + 2 i) x^{2} + 10 x + 2 = 0

替代

x = a + bi

(3 + 2 i) (a + bi)^{2} + 10 (a + bi) + 2 = 0

展开

(3 + 2 i) (a + bi)^{2} + 10 (a + bi) + 2 : (3 a^{2} - 3 b^{2} - 4 ab + 10 a + 2) + i (10 b + 2 a^{2} - 2 b^{2} + 6 ab)

(3 a^{2} - 3 b^{2} - 4 ab + 10 a + 2) + i (10 b + 2 a^{2} - 2 b^{2} + 6 ab) = 0

将

0

改写成标准复数形式:

0 + 0 i

(3 a^{2} - 3 b^{2} - 4 ab + 10 a + 2) + i (10 b + 2 a^{2} - 2 b^{2} + 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} - 4 ab + 10 a + 2 = 0 10 b + 2 a^{2} - 2 b^{2} + 6 ab = 0]

[3 a^{2} - 3 b^{2} - 4 ab + 10 a + 2 = 0 10 b + 2 a^{2} - 2 b^{2} + 6 ab = 0] : (a = - 0.21265 \dots, a = - 2.09503 \dots, b = - \frac{- 0.85061 \dots + 0.83297 \dots}{6} b = \frac{8.38015 \dots + 0.83297 \dots}{6})

x = a + bi

代回

x = - 0.21265 \dots - \frac{- 0.85061 \dots + 0.83297 \dots}{6} i, x = - 2.09503 \dots + \frac{8.38015 \dots + 0.83297 \dots}{6} i

流行的例子

a = bi

z^{2} + 2 i z - 5 = 0

0=x^2+(1-i)x+2-2i

0 = x^{2} + (1 - i) x + 2 - 2 i

x^{2} + x + i = 0

- 12 x + y i = 60 - 13 i