簡約 (i/(3-i))(1/(2+3i))

解

簡約

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

\frac{7}{130} + \frac{9}{130} i

解答ステップ

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

簡素化

(\frac{i}{3 - i}) (\frac{1}{2 + 3 i}) : \frac{i}{3 - i} \cdot \frac{1}{2 + 3 i}

= \frac{i}{3 - i} \cdot \frac{1}{2 + 3 i}

分数の規則を適用する:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

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

規則を適用する:

a \cdot 1 = a

i 1 = i

= \frac{i}{( 3 - i ) ( 2 + 3 i )}

(3 - i) (2 + 3 i) = 9 + 7 i

= \frac{i}{9 + 7 i}

共役で乗じる

\frac{9 - 7 i}{9 - 7 i}

= \frac{i ( 9 - 7 i )}{( 9 + 7 i ) ( 9 - 7 i )}

簡素化

\frac{i ( 9 - 7 i )}{( 9 + 7 i ) ( 9 - 7 i )} : \frac{9 i + 7}{130}

= \frac{9 i + 7}{130}

標準的な複素数形式で書き直す:

\frac{7}{130} + \frac{9}{130} i

= \frac{7}{130} + \frac{9}{130} i