x^2=1184-125.6637i

解答

x^{2} = 1184 - 125.6637 i

x = \frac{11840000 + 1.41765 E 14}{100 2} - \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14} i, x = - \frac{11840000 + 1.41765 E 14}{100 2} + \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14} i

求解步骤

x^{2} = 1184 - 125.6637 i

替代

x = a + bi

(a + bi)^{2} = 1184 - 125.6637 i

展开

(a + bi)^{2} : (a^{2} - b^{2}) + 2 iab

(a^{2} - b^{2}) + 2 iab = 1184 - 125.6637 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[a^{2} - b^{2} = 1184 2 ab = - 125.6637]

[a^{2} - b^{2} = 1184 2 ab = - 125.6637] : a = \frac{11840000 + 1.41765 E 14}{100 2}, a = - \frac{11840000 + 1.41765 E 14}{100 2}, b = - \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14} b = \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14}

x = a + bi

代回

x = \frac{11840000 + 1.41765 E 14}{100 2} - \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14} i, x = - \frac{11840000 + 1.41765 E 14}{100 2} + \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14} i

(x + 2 i) (y + 2 i) = \frac{16 i}{1 + i} - 9

so l v e f or x, z = \frac{x + 4 i}{1 + x i}

so l v e f or x, x^{2} = x (4 + 5 i) + 1

i = \frac{3 6}{( r - 2 )}

x + y i - \frac{1}{x + y i} = 1 + 4 i