簡約 (i/(1+i))^5

解

簡約

(\frac{i}{1 + i})^{5}

\frac{i ( - 1 + i )}{8}

解答ステップ

(\frac{i}{1 + i})^{5}

簡素化

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

= (\frac{i ( 1 - i )}{2})^{5}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( i ( 1 - i ) ) ^{5}}{2 ^{5}}

簡素化

(i (1 - i))^{5} : i (4 i - 4)

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

2^{5} = 32

= \frac{i ( 4 i - 4 )}{32}

簡素化

\frac{i ( 4 i - 4 )}{32} : \frac{i ( i - 1 )}{8}

= \frac{i ( i - 1 )}{8}

標準的な複素数形式で書き直す:

\frac{i ( - 1 + i )}{8}

= \frac{i ( - 1 + i )}{8}