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受欢迎的代数 >

Z^2=7+3i

解答

Z^{2} = 7 + 3 i

解答

Z = \frac{7 + 58}{2} + \frac{3}{2 7 + 58} i, Z = - \frac{7 + 58}{2} - \frac{3}{2 7 + 58} i

求解步骤

Z^{2} = 7 + 3 i

替代

Z = x + y i

(x + y i)^{2} = 7 + 3 i

展开

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

(x^{2} - y^{2}) + 2 i x y = 7 + 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} = 7 2 x y = 3]

[x^{2} - y^{2} = 7 2 x y = 3] : x = \frac{7 + 58}{2}, x = - \frac{7 + 58}{2}, y = \frac{3}{2 7 + 58} y = - \frac{3}{2 7 + 58}

Z = x + y i

代回

Z = \frac{7 + 58}{2} + \frac{3}{2 7 + 58} i, Z = - \frac{7 + 58}{2} - \frac{3}{2 7 + 58} i

流行的例子

15 - 3 y i = 12 x + 2 i

(x+yi)^2=-9-40i

(x + y i)^{2} = - 9 - 40 i

\frac{x ^{2}}{2 i} - 2 = 0

(x - y i)^{2} = - 8 - 6

x^2-7x+9yi=y^2i+20yi-12

x^{2} - 7 x + 9 y i = y^{2} i + 20 y i - 12