i(q)=3-q+q^2

解答

i (q) = 3 - q + q^{2}

q = 0.35615 \dots - 1.23801 \dots i, q = 0.64384 \dots + 2.23801 \dots i

求解步骤

i (q) = 3 - q + q^{2}

替代

q = x + y i

i (x + y i) = 3 - (x + y i) + (x + y i)^{2}

乘开

- y + i x = (3 - x + x^{2} - y^{2}) + i (- y + 2 x y)

复数仅在实部和虚部均相等时才相等改写为方程组:

[- y = 3 - x + x^{2} - y^{2} x = - y + 2 x y]

[- y = 3 - x + x^{2} - y^{2} x = - y + 2 x y] : (x = 0.35615 \dots, x = 0.64384 \dots, y = - 1.23801 \dots y = 2.23801 \dots)

q = x + y i

代回

q = 0.35615 \dots - 1.23801 \dots i, q = 0.64384 \dots + 2.23801 \dots i

x 3 + 2 x 2 + 5 s i x = 1

so l v e f or y, s i x^{2} + 8 y = y^{2}

(x + y i)^{2} = 2 + 2 i 3

- 3 + y i = x + 6 i

40 - w^{2} - 2 w \cdot i = 0