(x+y)+(x-y)i=2+5i

解答

(x + y) + (x - y) \cdot i = 2 + 5 \cdot i

x = \frac{7}{2}, y = - \frac{3}{2}

求解步骤

(x + y) + (x - y) i = 2 + 5 i

将

(x + y) + (x - y) \cdot i

改写成标准复数形式:

(x + y) + (x - y) i

(x + y) + (x - y) i = 2 + 5 i

将

2 + 5 \cdot i

改写成标准复数形式:

2 + 5 i

(x + y) + (x - y) i = 2 + 5 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[x + y = 2 x - y = 5]

[x + y = 2 x - y = 5] : x = \frac{7}{2}, y = - \frac{3}{2}

x = \frac{7}{2}, y = - \frac{3}{2}

(1 + i) (x + y i) = 1 + 3 i

4 z^{2} - 4 z + 3 - 23 i = 0

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

4 a - 3 i = 6 + bi

∣ a - i ∣ = 37