Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 329: 21

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

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