簡約 (3((4i)/n)^2+8((4i)/n)-5)(4/n)

解

簡約

(3 (\frac{4 i}{n})^{2} + 8 (\frac{4 i}{n}) - 5) (\frac{4}{n})

\frac{- 192 - 20 n ^{2}}{n ^{3}} + i \frac{128}{n ^{2}}

解答ステップ

(3 (\frac{4 i}{n})^{2} + 8 (\frac{4 i}{n}) - 5) (\frac{4}{n})

括弧を削除する:

(a) = a

= (3 (\frac{4 i}{n})^{2} + 8 \cdot \frac{4 i}{n} - 5) \frac{4}{n}

3 (\frac{4 i}{n})^{2} = - \frac{48}{n ^{2}}

= \frac{4}{n} (8 \cdot \frac{4 i}{n} - \frac{48}{n ^{2}} - 5)

8 \cdot \frac{4 i}{n} = \frac{32 i}{n}

= \frac{4}{n} (\frac{32 i}{n} - \frac{48}{n ^{2}} - 5)

分数を乗じる:

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

= \frac{4 ( - \frac{48}{n ^{2}} + \frac{32 i}{n} - 5 )}{n}

結合

- \frac{48}{n ^{2}} + \frac{32 i}{n} - 5 : \frac{- 48 + 32 in - 5 n ^{2}}{n ^{2}}

= \frac{4 \cdot \frac{- 5 n ^{2} + 32 in - 48}{n ^{2}}}{n}

乗じる

4 \cdot \frac{- 48 + 32 in - 5 n ^{2}}{n ^{2}} : \frac{4 ( - 5 n ^{2} + 32 in - 48 )}{n ^{2}}

= \frac{\frac{4 ( - 5 n ^{2} + 32 in - 48 )}{n ^{2}}}{n}

分数の規則を適用する:

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

= \frac{( - 48 + 32 in - 5 n ^{2} ) \cdot 4}{n ^{2} n}

n^{2} n = n^{3}

= \frac{4 ( - 5 n ^{2} + 32 in - 48 )}{n ^{3}}

標準的な複素数形式で

\frac{( - 48 + 32 in - 5 n ^{2} ) \cdot 4}{n ^{3}}

を書き換える:

\frac{- 192 - 20 n ^{2}}{n ^{3}} + \frac{128}{n ^{2}} i

= \frac{- 192 - 20 n ^{2}}{n ^{3}} + \frac{128}{n ^{2}} i