I'll use Sophie Germain's Identity for this problem and don't think it would be posssible to use the Simon's favorite factoring trick. The Simon's favorite factoring trick is only applicable in:

- Two variable problems

- Degree of no more than 2.

z^4 + 4(1^4) = (z^2 + 2z + 2)(z^2 - 2z + 2)

You can find the complex roots by using the quadratic formula from there.

For this problem, you can even use Roots of Unity: https://artofproblemsolving.com/wiki/index.php/Roots_of_unity.