What is expand ((1+j)^6)/((1-j)^2(sqrt(2)+j)^4) ?

The solution to expand ((1+j)^6)/((1-j)^2(sqrt(2)+j)^4) is

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expand ((1+j)^6)/((1-j)^2(sqrt(2)+j)^4)

expand

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

\frac{1 + 6 j + 15 j ^{2} + 20 j ^{3} + 15 j ^{4} + 6 j ^{5} + j ^{6}}{j ^{6} - 2 j ^{5} + 4 2 j ^{5} + 13 j ^{4} - 8 2 j ^{4} + 12 2 j ^{3} - 24 j ^{3} + 16 j ^{2} - 16 2 j ^{2} + 8 2 j - 8 j + 4}

Solution steps

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

(1 - j)^{2} = 1 - 2 j + j^{2}

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

(2 + j)^{4} = 4 + 82 j + 12 j^{2} + 42 j^{3} + j^{4}

= \frac{( 1 + j ) ^{6}}{( j ^{2} - 2 j + 1 ) ( j ^{4} + 4 2 j ^{3} + 12 j ^{2} + 8 2 j + 4 )}

(1 + j)^{6} = 1 + 6 j + 15 j^{2} + 20 j^{3} + 15 j^{4} + 6 j^{5} + j^{6}

= \frac{1 + 6 j + 15 j ^{2} + 20 j ^{3} + 15 j ^{4} + 6 j ^{5} + j ^{6}}{( j ^{2} - 2 j + 1 ) ( j ^{4} + 4 2 j ^{3} + 12 j ^{2} + 8 2 j + 4 )}

Expand

(1 - 2 j + j^{2}) (4 + 82 j + 12 j^{2} + 42 j^{3} + j^{4}) : j^{6} - 2 j^{5} + 42 j^{5} + 13 j^{4} - 82 j^{4} + 122 j^{3} - 24 j^{3} + 16 j^{2} - 162 j^{2} + 82 j - 8 j + 4

= \frac{1 + 6 j + 15 j ^{2} + 20 j ^{3} + 15 j ^{4} + 6 j ^{5} + j ^{6}}{j ^{6} - 2 j ^{5} + 4 2 j ^{5} + 13 j ^{4} - 8 2 j ^{4} + 12 2 j ^{3} - 24 j ^{3} + 16 j ^{2} - 16 2 j ^{2} + 8 2 j - 8 j + 4}

(3 x - 2)^{2}

(cos (θ) + i sin (θ))^{5}

2 (\frac{5}{e ^{4}} + \frac{5}{e ^{16}} + \frac{5}{e ^{36}})

(2 - 3 i)^{4}

sin (x) (sin (x) + 1)

What is expand ((1+j)^6)/((1-j)^2(sqrt(2)+j)^4) ?
The solution to expand ((1+j)^6)/((1-j)^2(sqrt(2)+j)^4) is