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受欢迎的代数 >

z^2-z-3iz+3i=0

解答

z^{2} - z - 3 i z + 3 i = 0

解答

z = 3 i, z = 1

求解步骤

z^{2} - z - 3 i z + 3 i = 0

替代

z = x + y i

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

展开

(x + y i)^{2} - (x + y i) - 3 i (x + y i) + 3 i : (x^{2} - y^{2} - x + 3 y) + i (3 - y - 3 x + 2 x y)

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

将

0

改写成标准复数形式:

0 + 0 i

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

[x^{2} - y^{2} - x + 3 y = 0 3 - y - 3 x + 2 x y = 0] : (x = 0, x = 1, y = 3 y = 0)

z = x + y i

代回

z = 3 i, z = 1

流行的例子

(2-i)^2-(2-yi)=x+5i

(2 - i)^{2} - (2 - y i) = x + 5 i

∣ z - (1 - i) ∣ = 2

a - bi = i (a + bi)

(z+1)/(z-1)=2+i^{25}

\frac{z + 1}{z - 1} = 2 + i^{25}

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

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