solvefor i= x/(ax+b),x

解答

求解

i = \frac{x}{a x + b}, x

无解

求解步骤

i = \frac{x}{a x + b}

替代

x = a + bi

i = \frac{a + bi}{a ( a + bi ) + b}

在两边乘以

aa + b + iab

i (aa + b + iab) = \frac{a + bi}{a ( a + bi ) + b} (aa + b + iab)

乘开

- ab + i (aa + b) = a + ib

复数仅在实部和虚部均相等时才相等改写为方程组:

[- ab = a aa + b = b]

[- ab = a aa + b = b] : 无解

x = a + bi

代回

无解

(1 + i) (a + bi) + 5 = 2 \cdot 3 i

r = 2 t i + (t^{2} - 1) j

- 6 i = \frac{- i}{120 π \cdot C}

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

x^{2} = - \frac{4}{3} i