(xi)^2+125.6637xi+1184=0

解

(x i)^{2} + 125.6637 x i + 1184 = 0

x = \frac{125.6637 + 11055.36549 \dots}{2} i, x = \frac{125.6637 - 11055.36549 \dots}{2} i

解答ステップ

(x i)^{2} + 125.6637 x i + 1184 = 0

代用

x = a + bi

((a + bi) i)^{2} + 125.6637 (a + bi) i + 1184 = 0

拡張

((a + bi) i)^{2} + 125.6637 (a + bi) i + 1184 : (b^{2} - a^{2} - 125.6637 b + 1184) + i (125.6637 a - 2 ab)

(b^{2} - a^{2} - 125.6637 b + 1184) + i (125.6637 a - 2 ab) = 0

標準的な複素数形式で

0

を書き換える:

0 + 0 i

(b^{2} - a^{2} - 125.6637 b + 1184) + i (125.6637 a - 2 ab) = 0 + 0 i

複素数は, その実数部と虚数部が等しい場合にのみ等しくなるequation系として書き換える:

[b^{2} - a^{2} - 125.6637 b + 1184 = 0 125.6637 a - 2 ab = 0]

[b^{2} - a^{2} - 125.6637 b + 1184 = 0 125.6637 a - 2 ab = 0] : (a = 0, a = 0, b = \frac{125.6637 + 11055.36549 \dots}{2} b = \frac{125.6637 - 11055.36549 \dots}{2})

代用を戻す

x = a + bi

x = \frac{125.6637 + 11055.36549 \dots}{2} i, x = \frac{125.6637 - 11055.36549 \dots}{2} i