Question

How do you simplify `(z^-1 + z^-3)^-2`?

Answer 1

`(z^(-1) +z^(-3))^(-2) =z^6/((z^2+1)^2)`

Explanation:

`(z^(-1) +z^(-3))^(-2) = 1/((z^(-1) +z^(-3))^2`

`=1/((1/z +1/z^3)^2) =1/((1/z^2 +2/z^4+1/z^6)`

`=1/((z^4 +2 z^2+1)/z^6)=z^6/((z^4 +2 z^2+1)`

`=z^6/((z^2+1)^2)` [Ans]