work

(4 x-i) (4 x+i)
(4 x-i) (4 x+i) = (4 x) (4 x) + (4 x) (i) + (-i) (4 x) + (-i) (i):
4×4 x x+i×4 x-i×4 x-i×i
4 x×4 x = 4×4 x^2:
4×4 x^2+i×4 x-i×4 x-i×i
4×4  =  16:
16 x^2+i×4 x-i×4 x-i×i
-i×i = -i^2:
16 x^2+i×4 x-i×4 x+-i^2
i^2 = -1:
16 x^2+i×4 x-i×4 x--1
(-1)^2 = 1:
16 x^2+i×4 x-i×4 x+1
Grouping like terms, 16 x^2+i×4 x-i×4 x+1 = 16 x^2+1+(4 i x-4 i x):
16 x^2+1+(4 i x-4 i x)
4 i x-4 i x = 0:
Answer:
 16 x^2+1