Most textbooks list the real part of the index of refraction. How would I go about calculating the imaginary part of the index of refraction of air?
The imaginary part is only non-zero very near to the absorption frequencies of the molecules. These absorptions occur in the infrared and ultraviolet, so you don't have to care about them in the visible. In the other ranges, the absorption coefficients are tabulated, so that you can calculate the imaginary part of the index of refraction if you like.