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受欢迎的代数 >

z^2+5z+15+3i=0

解答

z^{2} + 5 z + 15 + 3 i = 0

解答

z = - 2 - 3 i, z = - 3 + 3 i

求解步骤

z^{2} + 5 z + 15 + 3 i = 0

替代

z = x + y i

(x + y i)^{2} + 5 (x + y i) + 15 + 3 i = 0

展开

(x + y i)^{2} + 5 (x + y i) + 15 + 3 i : (x^{2} - y^{2} + 5 x + 15) + i (3 + 5 y + 2 x y)

(x^{2} - y^{2} + 5 x + 15) + i (3 + 5 y + 2 x y) = 0

将

0

改写成标准复数形式:

0 + 0 i

(x^{2} - y^{2} + 5 x + 15) + i (3 + 5 y + 2 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:

[x^{2} - y^{2} + 5 x + 15 = 0 3 + 5 y + 2 x y = 0]

[x^{2} - y^{2} + 5 x + 15 = 0 3 + 5 y + 2 x y = 0] : (x = - 2, x = - 3, y = - 3 y = 3)

z = x + y i

代回

z = - 2 - 3 i, z = - 3 + 3 i

流行的例子

(3k+2)+(4m)i=-4+20i

(3 k + 2) + (4 m) i = - 4 + 20 i

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

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

i(x)=-(x^2)/4+3450x

i (x) = - \frac{x ^{2}}{4} + 3450 x

(x - i) (x + i) = 0

x + y \cdot i = i