(x+iy)^2=1

解答

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

(x = 1, x = - 1, y = 0 y = 0)

求解步骤

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

展开

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

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

将

1

改写成标准复数形式:

1 + 0 i

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

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

(x = 1, x = - 1, y = 0 y = 0)

2 i x_{2} = - x_{3}

z^{2} - (5 - 2 i) z + (8 - 20 i) = 0

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

(4 - i) z + 5 w = 3 i

- \frac{1}{z - i} - (- 2) i - z = 0