i(x)=-x^2+80x+650

解

i (x) = - x^{2} + 80 x + 650

x = - 7.43340 \dots - 0.07835 \dots i, x = 87.43340 \dots - 0.92164 \dots i

解答ステップ

i (x) = - x^{2} + 80 x + 650

代用

x = a + bi

i (a + bi) = - (a + bi)^{2} + 80 (a + bi) + 650

拡張

- b + ia = (- a^{2} + b^{2} + 80 a + 650) + i (80 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} + 80 a + 650 a = 80 b - 2 ab]

[- b = - a^{2} + b^{2} + 80 a + 650 a = 80 b - 2 ab] : (a = - 7.43340 \dots, a = 87.43340 \dots, b = - 0.07835 \dots b = - 0.92164 \dots)

代用を戻す

x = a + bi

x = - 7.43340 \dots - 0.07835 \dots i, x = 87.43340 \dots - 0.92164 \dots i