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

解答

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

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

求解步骤

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

替代

x = a + bi

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

乘开

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

复数仅在实部和虚部均相等时才相等改写为方程组:

[- 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)

x = a + bi

代回

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

(1 + i) (x + 2 y) + (3 - 2 i) (x - y) = 8 + 3 i 3 i

3 x + (y - x) i = 6

4 x_{1} + 5 x_{2} = (1 + i) x_{1}

z^{2} - z - 1 + i = 0

+ i x^{2} = 1 - i, x^{1} = 1