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受欢迎的代数 >

z^2-2i=0

解答

z^{2} - 2 i = 0

解答

z = 1 + i, z = - 1 - i

求解步骤

z^{2} - 2 i = 0

替代

z = x + y i

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

展开

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

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

将

0

改写成标准复数形式:

0 + 0 i

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

[x^{2} - y^{2} = 0 - 2 + 2 x y = 0] : (x = 1, x = - 1, y = 1 y = - 1)

z = x + y i

代回

z = 1 + i, z = - 1 - i

流行的例子

x^2-(3+2i)x+1+3i=0

x^{2} - (3 + 2 i) x + 1 + 3 i = 0

-340i=X(10-159i)-Y(-159i)

- 340 i = X (10 - 159 i) - Y (- 159 i)

7x+2y-2i=3+(3x+1/5 y)i

7 x + 2 y - 2 i = 3 + (3 x + \frac{1}{5} y) i

ai+b+4=bi-2i+3a

ai + b + 4 = bi - 2 i + 3 a

z^{2} = 8 + 6 i