(2+3i)(a+bi)=13

解答

(2 + 3 i) (a + bi) = 13

a = 2, b = - 3

求解步骤

(2 + 3 i) (a + bi) = 13

展开

(2 + 3 i) (a + bi) : (2 a - 3 b) + i (2 b + 3 a)

(2 a - 3 b) + i (2 b + 3 a) = 13

将

13

改写成标准复数形式:

13 + 0 i

(2 a - 3 b) + i (2 b + 3 a) = 13 + 0 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[2 a - 3 b = 13 2 b + 3 a = 0]

[2 a - 3 b = 13 2 b + 3 a = 0] : a = 2, b = - 3

a = 2, b = - 3

22 (x + y i) + (28 + 4 i) = 72 - 62 i

a x^{2} - b x + 9 + 3 i = 0

2 i (a + bi) + 6 = 9 i + (a + bi)

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

(9 - 7 i) - 7 = x - (7 + y i)