Band pass filter (digital resonance)
Here is (I think) what you are supposed to be doing


Draw a diagram of the poles and the unit circle and zoom in on the area around the resonance frequency
Estimate the relative gain as the inverse of the distance between the pole and the unit circle (assuming that conjugate pole is too far away to change the gain much over a narrow frequency range)
Pencil in the -3dB points by, again, using distance as a representative for gain
Ignore the curvature of the circle (since r is close to 1)
Do some trigonometry to calculate the distance between the two -3dB points
Convert this distance to a frequency difference.