簡約 6/(9+i)

解

簡約

\frac{6}{9 + i}

\frac{27}{41} - \frac{3}{41} i

解答ステップ

\frac{6}{9 + i}

共役で乗じる

\frac{9 - i}{9 - i}

= \frac{6 ( 9 - i )}{( 9 + i ) ( 9 - i )}

簡素化

\frac{6 ( 9 - i )}{( 9 + i ) ( 9 - i )} : \frac{54 - 6 i}{82}

= \frac{54 - 6 i}{82}

分数の規則を適用する:

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

= \frac{54}{82} + \frac{- 6}{82} i

簡素化

\frac{54}{82} + \frac{- 6}{82} i : \frac{27}{41} - \frac{3}{41} i

= \frac{27}{41} - \frac{3}{41} i