(a+bi)^2=-4

解答

(a + bi)^{2} = - 4

(a = 0, a = 0, b = 2 b = - 2)

求解步骤

(a + bi)^{2} = - 4

展开

(a + bi)^{2} : (a^{2} - b^{2}) + 2 iab

(a^{2} - b^{2}) + 2 iab = - 4

将

- 4

改写成标准复数形式:

- 4 + 0 i

(a^{2} - b^{2}) + 2 iab = - 4 + 0 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[a^{2} - b^{2} = - 4 2 ab = 0]

[a^{2} - b^{2} = - 4 2 ab = 0] : (a = 0, a = 0, b = 2 b = - 2)

(a = 0, a = 0, b = 2 b = - 2)

m^{2} = i

(x - 3) + (8 - y) i = - 3 + 4 i

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

x + (2 - 3 i) y = 0

z^{2} - (3 + 4 i) z + (1 - 9 i) = 0