簡約 (a+bi)/(c+di)

解

簡約

\frac{a + bi}{c + d i}

\frac{a c + b d}{c ^{2} + d ^{2}} + \frac{- a d + b c}{c ^{2} + d ^{2}} i

解答ステップ

\frac{a + bi}{c + d i}

共役で乗じる

\frac{c - d i}{c - d i}

= \frac{( a + bi ) ( c - d i )}{( c + d i ) ( c - d i )}

簡素化

\frac{( a + bi ) ( c - d i )}{( c + d i ) ( c - d i )} : \frac{a c + b d + ( - a d + b c ) i}{c ^{2} + d ^{2}}

= \frac{a c + b d + ( - a d + b c ) i}{c ^{2} + d ^{2}}

標準的な複素数形式で書き直す:

\frac{a c + b d}{c ^{2} + d ^{2}} + \frac{- a d + b c}{c ^{2} + d ^{2}} i

= \frac{a c + b d}{c ^{2} + d ^{2}} + \frac{- a d + b c}{c ^{2} + d ^{2}} i