簡約 ((5+i)^2(3-2(4-i)))/((1+i)^3)

解

簡約

\frac{( 5 + i ) ^{2} ( 3 - 2 ( 4 - i ) )}{( 1 + i ) ^{3}}

\frac{69}{2} + \frac{71}{2} i

解答ステップ

\frac{( 5 + i ) ^{2} ( 3 - 2 ( 4 - i ) )}{( 1 + i ) ^{3}}

簡素化

(5 + i)^{2} (3 - 2 (4 - i)) : - 2 i - 140

= \frac{- 2 i - 140}{( 1 + i ) ^{3}}

拡張

(1 + i)^{3} : 2 i - 2

= \frac{- 2 i - 140}{2 i - 2}

因数

- 2 i - 140 : - 2 (i + 70)

= \frac{- 2 ( i + 70 )}{2 i - 2}

因数

2 i - 2 : 2 (i - 1)

= \frac{- 2 ( i + 70 )}{2 ( i - 1 )}

共通因数を約分する:

2

= \frac{- ( i + 70 )}{i - 1}

簡素化

\frac{- ( i + 70 )}{i - 1} : \frac{69}{2} + \frac{71}{2} i

= \frac{69}{2} + \frac{71}{2} i