Chapter 3 - Polynomial and Rational Functions - 3.3 Zeros of Polynomial Functions - 3.3 Exercises - Page 336: 38

$-i, \pm5i$.

Step 1. Use the given coefficients of the polynomial to set up a division as shown in the figure. Step 2. Perform synthetic divisions (note that $-i$ is also a zero) and find the quotient as $x^2+25$. Step 3. Solve $x^2+25=0$ to get $x=\pm5i$.