Chapter 3 - Polynomial and Rational Functions - Section 3.3 Complex Zeros; Fundamental Theorem of Algebra - 3.3 Assess Your Understanding - Page 231: 14

$2+i$ and $i$

The Conjugate Pairs Theorem states that when a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. This means that, when $(p +i \ q)$ is a zero of a polynomial function with a real number of the coefficients, then its conjugate $(p –i q)$, is also a zero of the function. We can notice that the function has a degree of $4$, so it has $4$ complex (including real) zeros. Since, $2$ zeros are already given, then the remaining $2$ zeros are: $2+i$ and $i$, the conjugates of $2-i$ and $-i$, by the Conjugate Pairs Theorem.