Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 329: 22

$P(x)=[x-(i+4)][x+(i-4)]$ The zeros of the function are: $\{4+i,4-i\}$ $x =4+i$ with multiplicity 1 $x = 4-i$ with multiplicity 1

Factor the polynomial completely to obtain: $P(x)=x^{2}-8x+17$ $P(x)=[x-(i+4)][x+(i-4)]$ Equate each unique factor to zero then solve each equation to obtain: $x-(i+4)=0 \rightarrow x=4+i$ $x+(i-4)=0 \rightarrow x=4-i$ The zeros of the function are: $\{4+i,4-i\}$ $x =4+i$ with multiplicity 1 $x = 4-i$ with multiplicity 1