z=(6+8ai)/(2-3i)

解答

z = \frac{6 + 8 ai}{2 - 3 i}

z = \frac{12 - 24 a}{13} + i \frac{18 + 16 a}{13}

求解步骤

z = \frac{6 + 8 ai}{2 - 3 i}

将

z

改写成标准复数形式:

x + y i

展开

\frac{6 + 8 ai}{2 - 3 i} : \frac{12 - 24 a}{13} + i \frac{18 + 16 a}{13}

z = \frac{12 - 24 a}{13} + i \frac{18 + 16 a}{13}

z^{2} = i ∣ z ∣^{2} - 4 i

z^{1} + z^{2} = (3 - 2 i) + (4 + 3 i)

z^{2} + (2 i + 7) \cdot z + 6 + 3 i = 0

so l v e f or x, d i rec t r i xx + 5 = 0

\frac{z}{1 + z} = - 1 + i