Answer: Hello there!
here we have the equation n^4 - 1
using the relation: [tex](a^{2} - b^{2}) = (a+b)*(a-b)[/tex]
we can write our equation as:
[tex](n^{4} - 1) = ((n^{2} )^{2} -1^{2} ) = (n^{2} + 1)(n^{2} - 1) = (n^{2} + 1)(n + 1)(n-1)[/tex]
and (n^2 + 1) has only complex roots, i and - i, then we can factorize this as (n -i)(n + i) = n*n + ni - ni (+i)*(-i) = (n^2 + 1)
then our equation is: [tex](n^{2} + 1)(n + 1)(n-1) = (n + i)(n - i)(n + 1)(n-1)[/tex]
