z+|z|=25-5i

解答

z + ∣ z ∣ = 25 - 5 i

z = 12 - 5 i

求解步骤

z + ∣ z ∣ = 25 - 5 i

替代

z = x + y i

x + y i + ∣ (x + y i) ∣ = 25 - 5 i

化简

x + y i + ∣ x + y i ∣ : (x + x^{2} + y^{2}) + i y

(x + x^{2} + y^{2}) + i y = 25 - 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 + x^{2} + y^{2} = 25 y = - 5]

[x + x^{2} + y^{2} = 25 y = - 5] : (x = 12, y = - 5)

z = x + y i

代回

z = 12 - 5 i

(3 l + 4) + (3 - m) i = 16 - 3 i

(- 1 + i) a + (1 + 2 i) b = 1

(3 + 2 i) (a + bi) + (5 + 2 i) = 3 - i

x^{2} = - 4 i

(a + bi)^{2} = 1