ix=x^2-2x+2

解

i x = x^{2} - 2 x + 2

x = 0.58120 \dots - 0.69389 \dots i, x = 1.41879 \dots + 1.69389 \dots i

解答ステップ

i x = x^{2} - 2 x + 2

代用

x = a + bi

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

拡張

- b + ia = (a^{2} - b^{2} - 2 a + 2) + i (- 2 b + 2 ab)

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 = a^{2} - b^{2} - 2 a + 2 a = - 2 b + 2 ab]

[- b = a^{2} - b^{2} - 2 a + 2 a = - 2 b + 2 ab] : (a = 0.58120 \dots, a = 1.41879 \dots, b = - 0.69389 \dots b = 1.69389 \dots)

代用を戻す

x = a + bi

x = 0.58120 \dots - 0.69389 \dots i, x = 1.41879 \dots + 1.69389 \dots i