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受欢迎的代数 >

z^2=9i

解答

z^{2} = 9 i

解答

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

求解步骤

z^{2} = 9 i

替代

z = x + y i

(x + y i)^{2} = 9 i

展开

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

(x^{2} - y^{2}) + 2 i x y = 9 i

将

9 i

改写成标准复数形式:

0 + 9 i

(x^{2} - y^{2}) + 2 i x y = 0 + 9 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 = 9]

[x^{2} - y^{2} = 0 2 x y = 9] : (x = \frac{3}{2}, x = - \frac{3}{2}, y = \frac{3}{2} y = - \frac{3}{2})

z = x + y i

代回

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

流行的例子

a + bi = 4

x^{2} = - 5 + 12 i

((x+yi))/((x-yi))=x-yi

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

(100)/(8+6i)x+(1-i)^3y=7

\frac{100}{8 + 6 i} x + (1 - i)^{3} y = 7

z^{2} + 16 i = 0