(1+ai)/(5+bi)=2+7i

解答

\frac{1 + ai}{5 + bi} = 2 + 7 i

a = \frac{263}{7}, b = \frac{9}{7}

求解步骤

\frac{1 + ai}{5 + bi} = 2 + 7 i

在两边乘以

5 + bi

\frac{1 + ai}{5 + bi} (5 + bi) = 2 (5 + bi) + 7 i (5 + bi)

乘开

1 + ia = (10 - 7 b) + i (35 + 2 b)

复数仅在实部和虚部均相等时才相等改写为方程组:

[1 = 10 - 7 b a = 35 + 2 b]

[1 = 10 - 7 b a = 35 + 2 b] : a = \frac{263}{7}, b = \frac{9}{7}

a = \frac{263}{7}, b = \frac{9}{7}

z - \frac{2}{z} = i + \frac{2}{i}

(2 + i) z^{2} + (1 - 7 i) z - 5 = 0

6 i - x + y i = 4 + 2 i

∣ z ∣ - z = 2 + i

so l v e f or x, x^{2} y^{2} + x sin (y) = 4