x+yi-1/(x+yi)=1+4i

解答

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

(x = - 0.07024 \dots, x = 1.07024 \dots, y = 0.24637 \dots y = 3.75362 \dots)

求解步骤

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

在两边乘以

x + y i

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

乘开

(x^{2} - y^{2} - 1) + 2 i x y = (x - 4 y) + i (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^{2} - y^{2} - 1 = x - 4 y 2 x y = y + 4 x]

[x^{2} - y^{2} - 1 = x - 4 y 2 x y = y + 4 x] : (x = - 0.07024 \dots, x = 1.07024 \dots, y = 0.24637 \dots y = 3.75362 \dots)

(x = - 0.07024 \dots, x = 1.07024 \dots, y = 0.24637 \dots y = 3.75362 \dots)

4 z^{2} + (4 - 4 i) z + 5 - 2 i = 0

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

0 = z^{2} + i z - 6

(7 + m) + (4 l - 10) i = 3 - 6 i

(- 2 - 6 i) - p (4 - 2 i) = q i