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

解答

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

x = - \frac{17}{19}, y = \frac{5}{19}

求解步骤

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

展开

5 i (x + i y) + 3 (x - i y) + i y : (- 5 y + 3 x) + i (- 2 y + 5 x)

(- 5 y + 3 x) + i (- 2 y + 5 x) = - 4 - 5 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[- 5 y + 3 x = - 4 - 2 y + 5 x = - 5]

[- 5 y + 3 x = - 4 - 2 y + 5 x = - 5] : x = - \frac{17}{19}, y = \frac{5}{19}

x = - \frac{17}{19}, y = \frac{5}{19}

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

15 + 8 i = a + bi