Chapter 4 - Polynomial and Rational Functions - 4.6 Complex Zeros; Fundamental Theorem of Algebra - 4.6 Assess Your Understanding - Page 241: 35

$\pm i,\pm2 i$ $f(x)=(x+i)(x-i)(x+2i)(x-2i)$

Step 1. Factor the function to get a zero $f(x)=(x^2+1)(x^2+4)$ Step 2. Solve $x^2+1=0$ to get $x=\pm i$ Step 3. Solve $x^2+4=0$ to get $x=\pm2 i$ Step 4. Thus $f(x)=(x+i)(x-i)(x+2i)(x-2i)$