find the remaining zeros of f.

Question

degree 4 zeros i, -18+i

enter the remaining zeros of f

please help me out!

Answer 1

complex roots always come in conjugate pairs,
so the roots are ±i and -18+i and -18-i

so you would have
(x+i)(x-i)(x+ 18-i)(x+18+i)=0
(x^2 + 1)(x^2 + 18x + xi + 18x + 324 + 18i - xi - 18i - i^2) = 0
(x^2 + 1)(x^2 + 36x +324 + 1) = 0
(x^2 + 1)(x^2 + 36x + 325) = 0

expand again, and simplify