簡約 (-5)/(5-4i)

解

簡約

\frac{- 5}{5 - 4 i}

- \frac{25}{41} - \frac{20}{41} i

解答ステップ

\frac{- 5}{5 - 4 i}

共役で乗じる

\frac{5 + 4 i}{5 + 4 i}

= \frac{- 5 ( 5 + 4 i )}{( 5 - 4 i ) ( 5 + 4 i )}

簡素化

\frac{- 5 ( 5 + 4 i )}{( 5 - 4 i ) ( 5 + 4 i )} : \frac{- 25 - 20 i}{41}

= \frac{- 25 - 20 i}{41}

分数の規則を適用する:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{- 25}{41} + \frac{- 20}{41} i

簡素化

\frac{- 25}{41} + \frac{- 20}{41} i : - \frac{25}{41} - \frac{20}{41} i

= - \frac{25}{41} - \frac{20}{41} i