2x^2=14x-30i

解答

2 x^{2} = 14 x - 30 i

x = - 0.47596 \dots + 1.88633 \dots i, x = 7.47596 \dots - 1.88633 \dots i

求解步骤

2 x^{2} = 14 x - 30 i

替代

x = a + bi

2 (a + bi)^{2} = 14 (a + bi) - 30 i

乘开

(2 a^{2} - 2 b^{2}) + 4 iab = 14 a + i (- 30 + 14 b)

复数仅在实部和虚部均相等时才相等改写为方程组:

[2 a^{2} - 2 b^{2} = 14 a 4 ab = - 30 + 14 b]

[2 a^{2} - 2 b^{2} = 14 a 4 ab = - 30 + 14 b] : (a = - 0.47596 \dots, a = 7.47596 \dots, b = 1.88633 \dots b = - 1.88633 \dots)

x = a + bi

代回

x = - 0.47596 \dots + 1.88633 \dots i, x = 7.47596 \dots - 1.88633 \dots i

s i f (x) = - 2 x + 5, E (s, x) = f (1) + f (- 1)

3 z^{2} + (2 - 3 i) z - 1 - 3 i = 0

r (t) = (2 t + 1) i + (t^{2} - 1) j

2 x + 51 = 4 (2 + y i) - 12

z^{2} - (1 + 9 i) z - 20 + 5 i = 0