(x+iy)/(1+x+iy)=3+4i

解答

\frac{x + i y}{1 + x + i y} = 3 + 4 i

x = - \frac{11}{10}, y = \frac{1}{5}

求解步骤

\frac{x + i y}{1 + x + i y} = 3 + 4 i

在两边乘以

1 + x + i y

\frac{x + i y}{1 + x + i y} (1 + x + i y) = 3 (1 + x + i y) + 4 i (1 + x + i y)

乘开

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

复数仅在实部和虚部均相等时才相等改写为方程组:

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

[x = 3 + 3 x - 4 y y = 4 + 3 y + 4 x] : x = - \frac{11}{10}, y = \frac{1}{5}

x = - \frac{11}{10}, y = \frac{1}{5}

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

3 x - 2 y i = 6 + 4 i

p (2 i + 6 j) + q (2 i - 4 j) = 6 i - 7 j

(3 + i) x^{2} + 10 x - (9 + 3 i) = 0

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