((-6i+n-3n+5))/(4+n^2)=0

解答

\frac{( - 6 i + n - 3 n + 5 )}{4 + n ^{2}} = 0

n = \frac{5}{2} - 3 i

求解步骤

\frac{( - 6 i + n - 3 n + 5 )}{4 + n ^{2}} = 0

替代

n = x + y i

\frac{- 6 i + x + y i - 3 ( x + y i ) + 5}{4 + ( x + y i ) ^{2}} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

展开

- 6 i + x + y i - 3 (x + y i) + 5 : (- 2 x + 5) + i (- 6 - 2 y)

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

将

0

改写成标准复数形式:

0 + 0 i

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

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

n = x + y i

代回

n = \frac{5}{2} - 3 i

z^{2} - \frac{2 i + 1}{2 - i} = 0

∣ x + y i ∣ = y - i x

\frac{( z - 2 i )}{( z + 2 )} = 4 i

- y + x i = x - y i

\frac{2 + ai}{4 + bi} = 2 + 5 i