(-1)/(b+i)= 1/(-b+i)

解答

\frac{- 1}{b + i} = \frac{1}{- b + i}

无解

求解步骤

\frac{- 1}{b + i} = \frac{1}{- b + i}

替代

b = x + y i

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

使用分式交叉相乘: 若

\frac{a}{b} = \frac{c}{d}

则

a \cdot d = b \cdot c

(- 1) (- (x + y i) + i) = (x + y i + i) \cdot 1

乘开

x + i (- 1 + y) = x + i (1 + y)

复数仅在实部和虚部均相等时才相等改写为方程组:

[x = x - 1 + y = 1 + y]

[x = x - 1 + y = 1 + y] : 无解

b = x + y i

代回

无解

(x + y) + (x - y) \cdot i = 2 + 5 \cdot i

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

4 z^{2} - 4 z + 3 - 23 i = 0

(x + y i) (2 + 3 i) = 1 - 5 i

4 a - 3 i = 6 + bi