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受欢迎的代数 >

(5i)/(4+9i)= a/b

解答

\frac{5 i}{4 + 9 i} = \frac{a}{b}

解答

a = 0, b = 0

求解步骤

\frac{5 i}{4 + 9 i} = \frac{a}{b}

使用分式交叉相乘: 若

\frac{a}{b} = \frac{c}{d}

则

a \cdot d = b \cdot c

5 ib = (4 + 9 i) a

展开

(4 + 9 i) a : 4 a + 9 ia

5 ib = 4 a + 9 ia

将

5 ib

改写成标准复数形式:

0 + 5 bi

0 + 5 bi = 4 a + 9 ia

复数仅在实部和虚部均相等时才相等改写为方程组:

[0 = 4 a 5 b = 9 a]

[0 = 4 a 5 b = 9 a] : a = 0, b = 0

a = 0, b = 0

流行的例子

(z-(1+2i))(z+(1+2i))=0

(z - (1 + 2 i)) (z + (1 + 2 i)) = 0

5 x - 2 y i = - 8 x + 9

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

4 + 3 i = x + y i

|2i+6j+k(2i-4j)|=5

∣ 2 i + 6 j + k (2 i - 4 j) ∣ = 5