i(x)=x^2+4x+7

解

i (x) = x^{2} + 4 x + 7

x = - 1.46798 \dots - 1.37963 \dots i, x = - 2.53201 \dots + 2.37963 \dots i

解答ステップ

i (x) = x^{2} + 4 x + 7

代用

x = a + bi

i (a + bi) = (a + bi)^{2} + 4 (a + bi) + 7

拡張

- b + ia = (a^{2} - b^{2} + 4 a + 7) + i (4 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} + 4 a + 7 a = 4 b + 2 ab]

[- b = a^{2} - b^{2} + 4 a + 7 a = 4 b + 2 ab] : (a = - 1.46798 \dots, a = - 2.53201 \dots, b = - 1.37963 \dots b = 2.37963 \dots)

代用を戻す

x = a + bi

x = - 1.46798 \dots - 1.37963 \dots i, x = - 2.53201 \dots + 2.37963 \dots i