i(x)=2000x-2x^2

解

i (x) = 2000 x - 2 x^{2}

x = 0, x = 1000 - \frac{1}{2} i

解答ステップ

i (x) = 2000 x - 2 x^{2}

代用

x = a + bi

i (a + bi) = 2000 (a + bi) - 2 (a + bi)^{2}

拡張

- b + ia = (2000 a - 2 a^{2} + 2 b^{2}) + i (2000 b - 4 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 = 2000 a - 2 a^{2} + 2 b^{2} a = 2000 b - 4 ab]

[- b = 2000 a - 2 a^{2} + 2 b^{2} a = 2000 b - 4 ab] : (a = 0.00000 \dots, a = 1000, b = 0 b = - \frac{1}{2})

代用を戻す

x = a + bi

x = 0, x = 1000 - \frac{1}{2} i