A polynomial function with rational coefficients has the following zeros. Find all additional zeros.

−3−i,−3+ √7

I'm using √ as a square root
I know 3 is a zero and so is i but i don't know the rest

Question

A polynomial function with rational coefficients has the following zeros. Find all additional zeros.

−3−i,−3+ √7

I'm using √ as a square root 
I know 3 is a zero and so is i but i don't know the rest

anonymous · Answer

if one zero is a+ib then it has also a-ib as the other zero
if one zero is of the form a+sqrt(b) then it has also a+sqrt(b)  as the other zero

anonymous · Answer

so it is 3, -3, i, -i

anonymous · Answer

in other words rational roots and imaginary roots occur in conjugate pairs

anonymous · Answer

−3+i,
−3- √7

anonymous · Answer

I'm sorry I'm being a hassle I'm trying to learn this for the first time