In order to factor this expression over the set of complex numbers, let's rewrite the second term as follows:
[tex]4b^2=-4b^2i^2[/tex]Then, we can use the following notable product:
[tex]m^2-n^2=(m+n)(m-n)[/tex]So we have:
[tex]\begin{gathered} 16a^4-4b^2i^2\\ \\ =(4a^2)^2-(2bi)^2\\ \\ =(4a^2+2bi)(4a^2-2bi) \end{gathered}[/tex]