(x+iy+2+3i)/(2x+2iy-3)=i+2

解答

\frac{x + i y + 2 + 3 i}{2 x + 2 i y - 3} = i + 2

x = \frac{36}{13}, y = \frac{2}{13}

求解步骤

\frac{x + i y + 2 + 3 i}{2 x + 2 i y - 3} = i + 2

在两边乘以

2 x - 3 + 2 i y

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

乘开

(x + 2) + i (3 + y) = (- 2 y + 4 x - 6) + i (- 3 + 2 x + 4 y)

复数仅在实部和虚部均相等时才相等改写为方程组:

[x + 2 = - 2 y + 4 x - 6 3 + y = - 3 + 2 x + 4 y]

[x + 2 = - 2 y + 4 x - 6 3 + y = - 3 + 2 x + 4 y] : x = \frac{36}{13}, y = \frac{2}{13}

x = \frac{36}{13}, y = \frac{2}{13}

so l v e f or t, a = v f - \frac{v i}{t}

1.2 x + 3 + y i = 7.2 - 4.3 i

i (x) = 3 x^{2} + 2 x - 1

\frac{18 + i}{4 + 3 i} = a + bi

(3 - i) (a + bi) = 0