(5+i2)/((-1+i6)x)=-1

解答

\frac{5 + i 2}{( - 1 + i 6 ) x} = - 1

x = - \frac{7}{37} + \frac{32}{37} i

求解步骤

\frac{5 + i 2}{( - 1 + i 6 ) x} = - 1

替代

x = a + bi

\frac{5 + i 2}{( - 1 + i 6 ) ( a + bi )} = - 1

在两边乘以

(- 1 + i 6) (a + bi)

\frac{5 + i 2}{( - 1 + i 6 ) ( a + bi )} (- 1 + i 6) (a + bi) = - 1 \cdot (- 1 + i 6) (a + bi)

乘开

5 + 2 i = (a + 6 b) + i (b - 6 a)

复数仅在实部和虚部均相等时才相等改写为方程组:

[5 = a + 6 b 2 = b - 6 a]

[5 = a + 6 b 2 = b - 6 a] : a = - \frac{7}{37}, b = \frac{32}{37}

x = a + bi

代回

x = - \frac{7}{37} + \frac{32}{37} i

5 i (x + i y) + 3 (x - i y) + i y = - 4 - 5 i

so l v e f or f, i f = M

- \frac{1}{z - 3 i} + 1 - z = 0

so l v e f or x, z = \frac{1 - x i}{1 + x i}

2 x^{2} + i x - 10 = 0