Express in the form`((a+ib)^3)/(a-ib)-((a-ib)^3)/(a+ib)`

Explanation

`((a+ib)^3)/(a-ib)-((a-ib)^3)/(a+ib)`
`=((a+ib)^4-(a-ib)^4)/((a-ib)(a+ib))`
`overset((a^4+4a^3ib+6a^2i^2b^2+4ai^3b^3+i^4b^4))underset(-(a^4-4a^3ib+6a^2i^2b^2-4ai^3b^3+i^4b^4))"/(a^2-i^2b^2)`
`=(8a^3ib+8ai^3b^3)/(a^2+b^2)=(8a^3ib-8aib^3)/(a^2+b^2)`
`(8abi(a^2-b^2))/(a^2=b^2)=0+(8ab(a^2-b^2)i)/(a^2+b^2)`