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受欢迎的代数 >

z^2=-2/3 i

解答

z^{2} = - \frac{2}{3} i

解答

z = \frac{1}{3} - \frac{3 \frac{2}{3}}{2} i, z = - \frac{1}{3} + \frac{3 \frac{2}{3}}{2} i

求解步骤

z^{2} = - \frac{2}{3} i

替代

z = x + y i

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

展开

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

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

将

- \frac{2}{3} i

改写成标准复数形式:

0 - \frac{2}{3} i

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

[x^{2} - y^{2} = 0 2 x y = - \frac{2}{3}] : x = \frac{1}{3}, x = - \frac{1}{3}, y = - \frac{3 \frac{2}{3}}{2} y = \frac{3 \frac{2}{3}}{2}

z = x + y i

代回

z = \frac{1}{3} - \frac{3 \frac{2}{3}}{2} i, z = - \frac{1}{3} + \frac{3 \frac{2}{3}}{2} i

流行的例子

W^{2} = 3 + 4 i

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

solvefor x,x^2y+sin(y)=c

so l v e f or x, x^{2} y + sin (y) = c

z^2-(5+i)z+8+i=0

z^{2} - (5 + i) z + 8 + i = 0

4 i - 10 = 2 x + y i + 8