簡約 (2/3+12i}{-7+\frac{1i)/4}

解

簡約

\frac{\frac{2}{3} + 12 i}{- 7 + \frac{1 i}{4}}

- \frac{16}{471} - \frac{808}{471} i

解答ステップ

\frac{\frac{2}{3} + 12 i}{- 7 + \frac{1 i}{4}}

標準的な複素数形式で

- 7 + \frac{1 i}{4}

を書き換える:

- 7 + \frac{1}{4} i

= \frac{\frac{2}{3} + 12 i}{- 7 + \frac{1}{4} i}

共役で乗じる

\frac{- 7 - \frac{1}{4} i}{- 7 - \frac{1}{4} i}

= \frac{( \frac{2}{3} + 12 i ) ( - 7 - \frac{1}{4} i )}{( - 7 + \frac{1}{4} i ) ( - 7 - \frac{1}{4} i )}

簡素化

\frac{( \frac{2}{3} + 12 i ) ( - 7 - \frac{1}{4} i )}{( - 7 + \frac{1}{4} i ) ( - 7 - \frac{1}{4} i )} : \frac{- \frac{5}{3} - \frac{505}{6} i}{\frac{785}{16}}

= \frac{- \frac{5}{3} - \frac{505}{6} i}{\frac{785}{16}}

分数の規則を適用する:

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

= \frac{- \frac{5}{3}}{\frac{785}{16}} + \frac{- \frac{505}{6}}{\frac{785}{16}} i

簡素化

\frac{- \frac{5}{3}}{\frac{785}{16}} + \frac{- \frac{505}{6}}{\frac{785}{16}} i : - \frac{16}{471} - \frac{808}{471} i

= - \frac{16}{471} - \frac{808}{471} i