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

解答

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

x = 2, y = 1

求解步骤

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

将

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

改写成标准复数形式:

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

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

复数仅在实部和虚部均相等时才相等改写为方程组:

[x - y = 1 x + 2 y = 4]

[x - y = 1 x + 2 y = 4] : x = 2, y = 1

x = 2, y = 1

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

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

(2 + i) x - y = 0

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

(x^{2} - 9) + (2 y - 5) i = 7 i