簡約 (2-i)/(3-i)-1/5 ((1+8i)/(1+3i))

解

簡約

\frac{2 - i}{3 - i} - \frac{1}{5} (\frac{1 + 8 i}{1 + 3 i})

\frac{1}{5} - \frac{1}{5} i

解答ステップ

\frac{2 - i}{3 - i} - \frac{1}{5} (\frac{1 + 8 i}{1 + 3 i})

\frac{2 - i}{3 - i} = \frac{7 - i}{10}

\frac{1 + 8 i}{1 + 3 i} = \frac{25 + 5 i}{10}

= \frac{7 - i}{10} - \frac{1}{5} \cdot \frac{25 + 5 i}{10}

簡素化

\frac{1}{5} \cdot \frac{25 + 5 i}{10} : \frac{\frac{5}{2} + \frac{1}{2} i}{5}

= \frac{7 - i}{10} - \frac{\frac{5}{2} + \frac{1}{2} i}{5}

結合

\frac{7 - i}{10} - \frac{\frac{5}{2} + \frac{1}{2} i}{5} : \frac{- i + 1}{5}

= \frac{- i + 1}{5}

標準的な複素数形式で書き直す:

\frac{1}{5} - \frac{1}{5} i

= \frac{1}{5} - \frac{1}{5} i