Second Order Transfer Function : Imaginary component in $R$?
HINT:

If you're looking for the zeros of $H(z)$, try $z_0=1$ or $z_0=-1$. If that works, try to figure out why, and derive it yourself. Then, think about what the magnitude and the phase of those zeros might be.

EDIT (in reaction to your comment): If you have a second-order polynomial with real-valued coefficients, then two complex conjugated zeros are not the only option; you can also have two real-valued zeros.