i(x)=3x^2+2x-1

解答

i (x) = 3 x^{2} + 2 x - 1

x = 0.31777 \dots + 0.08134 \dots i, x = - 0.98444 \dots + 0.25199 \dots i

求解步骤

i (x) = 3 x^{2} + 2 x - 1

替代

x = a + bi

i (a + bi) = 3 (a + bi)^{2} + 2 (a + bi) - 1

乘开

- b + ia = (3 a^{2} - 3 b^{2} + 2 a - 1) + i (2 b + 6 ab)

复数仅在实部和虚部均相等时才相等改写为方程组:

[- b = 3 a^{2} - 3 b^{2} + 2 a - 1 a = 2 b + 6 ab]

[- b = 3 a^{2} - 3 b^{2} + 2 a - 1 a = 2 b + 6 ab] : (a = 0.31777 \dots, a = - 0.98444 \dots, b = 0.08134 \dots b = 0.25199 \dots)

x = a + bi

代回

x = 0.31777 \dots + 0.08134 \dots i, x = - 0.98444 \dots + 0.25199 \dots i

\frac{18 + i}{4 + 3 i} = a + bi

(3 - i) (a + bi) = 0

x + i y = y + i x

(2 - 5 i) x + (1 + 3 i) y = 8 - 9 i

(z - i)^{2} = 3 + 4 i