erweitern ((1-j)^9)/((1+j)^7)

Lösung

erweitern

\frac{( 1 - j ) ^{9}}{( 1 + j ) ^{7}}

\frac{1 - 9 j + 36 j ^{2} - 84 j ^{3} + 126 j ^{4} - 126 j ^{5} + 84 j ^{6} - 36 j ^{7} + 9 j ^{8} - j ^{9}}{1 + 7 j + 21 j ^{2} + 35 j ^{3} + 35 j ^{4} + 21 j ^{5} + 7 j ^{6} + j ^{7}}

Schritte zur Lösung

\frac{( 1 - j ) ^{9}}{( 1 + j ) ^{7}}

(1 + j)^{7} = 1 + 7 j + 21 j^{2} + 35 j^{3} + 35 j^{4} + 21 j^{5} + 7 j^{6} + j^{7}

= \frac{( 1 - j ) ^{9}}{1 + 7 j + 21 j ^{2} + 35 j ^{3} + 35 j ^{4} + 21 j ^{5} + 7 j ^{6} + j ^{7}}

(1 - j)^{9} = 1 - 9 j + 36 j^{2} - 84 j^{3} + 126 j^{4} - 126 j^{5} + 84 j^{6} - 36 j^{7} + 9 j^{8} - j^{9}

= \frac{1 - 9 j + 36 j ^{2} - 84 j ^{3} + 126 j ^{4} - 126 j ^{5} + 84 j ^{6} - 36 j ^{7} + 9 j ^{8} - j ^{9}}{1 + 7 j + 21 j ^{2} + 35 j ^{3} + 35 j ^{4} + 21 j ^{5} + 7 j ^{6} + j ^{7}}

e x p an d \frac{x ^{2} - 3 x + 10}{( 3 - x ) x ^{2}}

e x p an d \frac{( 1 + 6 x )}{( ( 4 x - 3 ) ( 2 x + 5 ) )}

e x p an d (x + 1)^{2} d x

e x p an d \frac{8 e ^{- 2 t} ( 1 + 23 t )}{5}

e x p an d \frac{a ( b - 2 )}{c - 3}