x^2=4+4sqrt(15)i

解答

x^{2} = 4 + 415 i

x = 10 + 6 i, x = - 10 - 6 i

求解步骤

x^{2} = 4 + 415 i

替代

x = a + bi

(a + bi)^{2} = 4 + 415 i

展开

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

(a^{2} - b^{2}) + 2 iab = 4 + 415 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} = 4 2 ab = 415]

[a^{2} - b^{2} = 4 2 ab = 415] : (a = 10, a = - 10, b = 6 b = - 6)

x = a + bi

代回

x = 10 + 6 i, x = - 10 - 6 i

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

z^{2} + 4 i z - 1 = 0

so l v e f or c, z = \frac{- 3 + 3 i}{2 - c}

z^{2} = - 15 + 8 i

\frac{( - 6 i + n - 3 n + 5 )}{4 + n ^{2}} = 0