Are there imaginary infinities? Is this a meaningful concept?
For example, are there things that when graphed on the complex plane would produce an asymptote in the imaginary direction?
You’re question isn’t really clear, but yes to the extent there are real number infinities there are imaginary infinities. b*i goes to “imaginary infinity” as real b goes to infinity.
In another context, the Reimann sphere, there is a single point at infinity for the entire complex plane. It’s neither imaginary nor real or both just like zero is neither or both.