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受欢迎的代数 >

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

解答

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

解答

z = - 0.25706 \dots + 1.52908 \dots i, z = - 0.74293 \dots - 0.52908 \dots i

求解步骤

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

替代

z = x + y i

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

展开

(x + y i)^{2} + (1 - i) (x + y i) + 1 - i : (x^{2} - y^{2} + x + y + 1) + i (- 1 - x + y + 2 x y)

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

将

0

改写成标准复数形式:

0 + 0 i

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

[x^{2} - y^{2} + x + y + 1 = 0 - 1 - x + y + 2 x y = 0]

[x^{2} - y^{2} + x + y + 1 = 0 - 1 - x + y + 2 x y = 0] : (x = - 0.25706 \dots, x = - 0.74293 \dots, y = 1.52908 \dots y = - 0.52908 \dots)

z = x + y i

代回

z = - 0.25706 \dots + 1.52908 \dots i, z = - 0.74293 \dots - 0.52908 \dots i

流行的例子

\frac{1}{i C} = - 0.035 i

x + i y + i x + y = 2 + i

(3x-2yi)^2=(200)/(4+3i)

(3 x - 2 y i)^{2} = \frac{200}{4 + 3 i}

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

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

∣ z ∣ = 2 - 3 i + z