xi(x+3y)=(1+yi)(3x+4i)

解答

x i (x + 3 y) = (1 + y i) (3 x + 4 i)

(x = - 2, x = 2, y = - \frac{3}{2} y = \frac{3}{2})

求解步骤

x i (x + 3 y) = (1 + y i) (3 x + 4 i)

乘开

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

将

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

改写成标准复数形式:

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

0 + (x^{2} + 3 x y) i = (3 x - 4 y) + i (4 + 3 x y)

复数仅在实部和虚部均相等时才相等改写为方程组:

[0 = 3 x - 4 y x^{2} + 3 x y = 4 + 3 x y]

[0 = 3 x - 4 y x^{2} + 3 x y = 4 + 3 x y] : (x = - 2, x = 2, y = - \frac{3}{2} y = \frac{3}{2})

(x = - 2, x = 2, y = - \frac{3}{2} y = \frac{3}{2})

x^{2} - 3 - 3 i = 0

3 x^{2} + 6 i x = 0

- 4 i = \frac{1}{( 1000 \cdot x ) i}

i = - 24 t^{2} + 333 t - 32

(5 - \frac{1}{2} x) + (y - 1) i = 7 - 2 i