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受欢迎的代数 >

化简 |((1+i)^6)/((1-i)^2(sqrt(2)+i)^4)|

解答

化简

\frac{( 1 + i ) ^{6}}{( 1 - i ) ^{2} ( 2 + i ) ^{4}}

解答

\frac{4 ( - 7 - 4 2 i )}{81}

求解步骤

\frac{( 1 + i ) ^{6}}{( 1 - i ) ^{2} ( 2 + i ) ^{4}}

展开

(1 + i)^{6} : - 8 i

= \frac{- 8 i}{( 1 - i ) ^{2} ( 2 + i ) ^{4}}

化简

(1 - i)^{2} (2 + i)^{4} : - 2 i (42 i - 7)

= \frac{- 8 i}{- 2 i ( 4 2 i - 7 )}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

\frac{- 8 i}{- 2 i ( 4 2 i - 7 )} = \frac{8 i}{2 i ( 4 2 i - 7 )}

= \frac{8 i}{2 i ( 4 2 i - 7 )}

约分:

i

= \frac{8}{2 ( 4 2 i - 7 )}

因式分解数字:

8 = 2 \cdot 4

= \frac{2 \cdot 4}{2 ( 4 2 i - 7 )}

约分:

2

= \frac{4}{4 2 i - 7}

化简

\frac{4}{4 2 i - 7} : \frac{4 ( - 7 - 4 2 i )}{81}

= \frac{4 ( - 7 - 4 2 i )}{81}

流行的例子

展开 2(n(m+1))

e x p an d 2 (n (m + 1))

展开 1/((s+1)*(s+2))

e x p an d \frac{1}{( s + 1 ) \cdot ( s + 2 )}

展开 (x^{1/2}+x^{2/3})^9

e x p an d (x^{\frac{1}{2}} + x^{\frac{2}{3}})^{9}

展开 (x+sqrt(5))(x-sqrt(7))

e x p an d (x + 5) (x - 7)

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