簡約 (-2+i)/(6-10i)

解

簡約

\frac{- 2 + i}{6 - 10 i}

- \frac{11}{68} - \frac{7}{68} i

解答ステップ

\frac{- 2 + i}{6 - 10 i}

共役で乗じる

\frac{6 + 10 i}{6 + 10 i}

= \frac{( - 2 + i ) ( 6 + 10 i )}{( 6 - 10 i ) ( 6 + 10 i )}

簡素化

\frac{( - 2 + i ) ( 6 + 10 i )}{( 6 - 10 i ) ( 6 + 10 i )} : \frac{- 22 - 14 i}{136}

= \frac{- 22 - 14 i}{136}

分数の規則を適用する:

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

= \frac{- 22}{136} + \frac{- 14}{136} i

簡素化

\frac{- 22}{136} + \frac{- 14}{136} i : - \frac{11}{68} - \frac{7}{68} i

= - \frac{11}{68} - \frac{7}{68} i