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受欢迎的代数 >

3z^2-2+z-3iz^2+2i+zi=0

解答

3 z^{2} - 2 + z - 3 i z^{2} + 2 i + z i = 0

解答

z = \frac{23}{6} - \frac{1}{6} i, z = - \frac{23}{6} - \frac{1}{6} i

求解步骤

3 z^{2} - 2 + z - 3 i z^{2} + 2 i + z i = 0

替代

z = x + y i

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

展开

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

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

将

0

改写成标准复数形式:

0 + 0 i

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

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

[3 x^{2} - 3 y^{2} - 2 + x + 6 x y - y = 0 2 + x + y - 3 x^{2} + 3 y^{2} + 6 x y = 0] : (x = \frac{23}{6}, x = - \frac{23}{6}, y = - \frac{1}{6} y = - \frac{1}{6})

z = x + y i

代回

z = \frac{23}{6} - \frac{1}{6} i, z = - \frac{23}{6} - \frac{1}{6} i

流行的例子

∣ z + 3 ∣ = 1 - i z

2 x + 8 i = 6 - (2 y) i

9x+(y)i-5=-12i+4

9 x + (y) i - 5 = - 12 i + 4

i = (a + bi)^{2}

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

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