Hi,

point of this question is if one of answer is -i you can be assure +i is also one of another zeros

x= -1. X=3. X= i. X= -i

f(x)= (x + 1) (x - 3) (x - i) (x + i)

f(x)= (x2 -2x -3)(x2 + 1)

f(x)= x4 -2x3 -2x2 -2x -3

NOTE: if one of zeros is a + bi, certainly you have a - bi as a other zeros ( at polynomial function with rational coefficient)

I hope it is useful,

Minoo