Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 329: 31

$P(x)=(x-i)(x+i)$ The zeros of the function are: $\{i,-i)\}$ $x =-i$ with multiplicity 1 $x =i$ with multiplicity 1

Factor the polynomial completely to obtain: $P(x)=x^{4}+2x^{2}+1$ $P(x)=(x^{2}+1)^{2}$ $P(x)=(x-i)(x+i)$ Equate each unique factor to zero then solve each equation to obtain: $x-i=0 \rightarrow x=i$ $x+i=0 \rightarrow x=-i$ The zeros of the function are: $\{i,-i)\}$ $x =-i$ with multiplicity 1 $x =i$ with multiplicity 1