因式分解 (-1-9i)/(-2-9i)

解答

因式分解

\frac{- 1 - 9 i}{- 2 - 9 i}

\frac{83}{85} + i \frac{9}{85}

求解步骤

\frac{- 1 - 9 i}{- 2 - 9 i}

使用复数算数法则:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = - 1, b = - 9, c = - 2, d = - 9

= \frac{( - 1 \cdot ( - 2 ) + ( - 9 ) ( - 9 ) ) + ( - 9 ( - 2 ) - ( - 1 ) ( - 9 ) ) i}{( - 2 ) ^{2} + ( - 9 ) ^{2}}

整理后得

= \frac{83 + 9 i}{85}

将

\frac{83 + 9 i}{85}

改写成标准复数形式:

\frac{83}{85} + \frac{9}{85} i

= \frac{83}{85} + \frac{9}{85} i

f a c t or - 23 + 2 i

f a c t or - \infty - \infty + \infty

f a c t or 7 (6^{2} - 2 \cdot 6 + 91)

f (m) = m^{(2)} + 3 m + 9

f a c t or 2 \cdot (+ π)