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受欢迎的代数 >

z^2-8z+18=8i

解答

z^{2} - 8 z + 18 = 8 i

解答

z = 2.23276 \dots - 2.26342 \dots i, z = 5.76723 \dots + 2.26342 \dots i

求解步骤

z^{2} - 8 z + 18 = 8 i

替代

z = x + y i

(x + y i)^{2} - 8 (x + y i) + 18 = 8 i

展开

(x + y i)^{2} - 8 (x + y i) + 18 : (x^{2} - y^{2} - 8 x + 18) + i (- 8 y + 2 x y)

(x^{2} - y^{2} - 8 x + 18) + i (- 8 y + 2 x y) = 8 i

将

8 i

改写成标准复数形式:

0 + 8 i

(x^{2} - y^{2} - 8 x + 18) + i (- 8 y + 2 x y) = 0 + 8 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[x^{2} - y^{2} - 8 x + 18 = 0 - 8 y + 2 x y = 8]

[x^{2} - y^{2} - 8 x + 18 = 0 - 8 y + 2 x y = 8] : (x = 2.23276 \dots, x = 5.76723 \dots, y = - 2.26342 \dots y = 2.26342 \dots)

z = x + y i

代回

z = 2.23276 \dots - 2.26342 \dots i, z = 5.76723 \dots + 2.26342 \dots i

流行的例子

(-1+i)x+(1+i2)y=1

(- 1 + i) x + (1 + i 2) y = 1

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

solvefor z,z-1/z =5+4i

so l v e f or z, z - \frac{1}{z} = 5 + 4 i

∣ z - i ∣ = 4

(1+i)x-(1-2i)y=1+4i

(1 + i) x - (1 - 2 i) y = 1 + 4 i