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受欢迎的代数 >

((41+3i))/(65)= 1/x

解答

\frac{( 41 + 3 i )}{65} = \frac{1}{x}

解答

x = \frac{41}{26} - \frac{3}{26} i

求解步骤

\frac{( 41 + 3 i )}{65} = \frac{1}{x}

替代

x = a + bi

\frac{41 + 3 i}{65} = \frac{1}{a + bi}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

(41 + 3 i) (a + bi) = 65 \cdot 1

乘开

(41 a - 3 b) + i (3 a + 41 b) = 65

将

65

改写成标准复数形式:

65 + 0 i

(41 a - 3 b) + i (3 a + 41 b) = 65 + 0 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[41 a - 3 b = 65 3 a + 41 b = 0]

[41 a - 3 b = 65 3 a + 41 b = 0] : a = \frac{41}{26}, b = - \frac{3}{26}

x = a + bi

代回

x = \frac{41}{26} - \frac{3}{26} i

流行的例子

ix^2-2(i+1)x+10=0

i x^{2} - 2 (i + 1) x + 10 = 0

s i y = 33 y + 1

(1+4i)/(3-6i)=a+bi

\frac{1 + 4 i}{3 - 6 i} = a + bi

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a^2+2abi-b^2=2i

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