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受欢迎的代数 >

i(x)=x^2+4x+7

解答

i (x) = x^{2} + 4 x + 7

解答

x = - 1.46798 \dots - 1.37963 \dots i, x = - 2.53201 \dots + 2.37963 \dots i

求解步骤

i (x) = x^{2} + 4 x + 7

替代

x = a + bi

i (a + bi) = (a + bi)^{2} + 4 (a + bi) + 7

乘开

- b + ia = (a^{2} - b^{2} + 4 a + 7) + i (4 b + 2 ab)

复数仅在实部和虚部均相等时才相等改写为方程组:

[- b = a^{2} - b^{2} + 4 a + 7 a = 4 b + 2 ab]

[- b = a^{2} - b^{2} + 4 a + 7 a = 4 b + 2 ab] : (a = - 1.46798 \dots, a = - 2.53201 \dots, b = - 1.37963 \dots b = 2.37963 \dots)

x = a + bi

代回

x = - 1.46798 \dots - 1.37963 \dots i, x = - 2.53201 \dots + 2.37963 \dots i

流行的例子

z=sqrt(2)e^{i(pi/3)}

z = 2 e^{i (\frac{π}{3})}

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

z^2=2+2isqrt(3)

z^{2} = 2 + 2 i 3

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

6 + (x + 3 y) i = x + 3 i