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受欢迎的代数 >

solvefor z,z^2-2z+i=0

解答

求解

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

解答

z = - 0.09868 \dots + 0.45508 \dots i, z = 2.09868 \dots - 0.45508 \dots i

求解步骤

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

替代

z = x + y i

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

展开

(x + y i)^{2} - 2 (x + y i) + i : (x^{2} - y^{2} - 2 x) + i (1 - 2 y + 2 x y)

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

将

0

改写成标准复数形式:

0 + 0 i

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

[x^{2} - y^{2} - 2 x = 0 1 - 2 y + 2 x y = 0] : (x = - 0.09868 \dots, x = 2.09868 \dots, y = 0.45508 \dots y = - 0.45508 \dots)

z = x + y i

代回

z = - 0.09868 \dots + 0.45508 \dots i, z = 2.09868 \dots - 0.45508 \dots i

流行的例子

(i2j^3k)*(-ijk)=0

(i 2 j^{3} k) \cdot (- ijk) = 0

+10iez^2=-9+3i,z^1=10

+ 10 i e z^{2} = - 9 + 3 i, z^{1} = 10

(\frac{i}{h}) (\frac{4}{3}) = 1

x + y i = 2 + 3 i

solvefor x,(i(x-y))^2=2

so l v e f or x, (i (x - y))^{2} = 2