find remaining zeros

Question

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.

Degree 4;   zeros: i , 11 + i

Enter the remaining zeros of f.

Answer 1

This deals with knowing that complex zeros come in conjugate pairs. Conjugates are of the form a+bi and a-bi. Here, if i is a zero, then -i is also a zero. Similarly, if 11+i is a zero, then 11-i is a zero as well.