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受欢迎的代数 >

-3iw^2-16w+53i=0

解答

- 3 i w^{2} - 16 w + 53 i = 0

解答

w = \frac{95}{3} + \frac{8}{3} i, w = - \frac{95}{3} + \frac{8}{3} i

求解步骤

- 3 i w^{2} - 16 w + 53 i = 0

替代

w = x + y i

- 3 i (x + y i)^{2} - 16 (x + y i) + 53 i = 0

展开

- 3 i (x + y i)^{2} - 16 (x + y i) + 53 i : (6 x y - 16 x) + i (53 - 16 y - 3 x^{2} + 3 y^{2})

(6 x y - 16 x) + i (53 - 16 y - 3 x^{2} + 3 y^{2}) = 0

将

0

改写成标准复数形式:

0 + 0 i

(6 x y - 16 x) + i (53 - 16 y - 3 x^{2} + 3 y^{2}) = 0 + 0 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[6 x y - 16 x = 0 53 - 16 y - 3 x^{2} + 3 y^{2} = 0]

[6 x y - 16 x = 0 53 - 16 y - 3 x^{2} + 3 y^{2} = 0] : (x = \frac{95}{3}, x = - \frac{95}{3}, y = \frac{8}{3} y = \frac{8}{3})

w = x + y i

代回

w = \frac{95}{3} + \frac{8}{3} i, w = - \frac{95}{3} + \frac{8}{3} i

流行的例子

z \cdot z + z - 5 - 5 i = 0

i z^{2} - z + i = 0

z^{2} - 2 z + 1 - 2 i = 0

z^{2} - 2 z - 4 i = 2

(4+3i)/(m+ni)=1+2i

\frac{4 + 3 i}{m + ni} = 1 + 2 i