(3x-4y)+(6x+2y)i=5i

解答

(3 x - 4 y) + (6 x + 2 y) i = 5 i

x = \frac{2}{3}, y = \frac{1}{2}

求解步骤

(3 x - 4 y) + (6 x + 2 y) i = 5 i

将

5 i

改写成标准复数形式:

0 + 5 i

(3 x - 4 y) + (6 x + 2 y) i = 0 + 5 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[3 x - 4 y = 0 6 x + 2 y = 5]

[3 x - 4 y = 0 6 x + 2 y = 5] : x = \frac{2}{3}, y = \frac{1}{2}

x = \frac{2}{3}, y = \frac{1}{2}

z^{2} = 1 - 3 i

(1 + 3 i)^{11} = a + ib

∣ z - i ∣ = 5

z = 6 e^{\frac{π}{3} i}

z^{2} - i = 0