What do you mean by 'imaginary infinities'?
Even in the definition of integration, there is an infinite limit used. And integration is necessary for any physics that uses calculus.
A book on solid state physics will typically talk about an infinite lattice of atoms, for example. This simplifies the calculations and gives accurate results, It is certainly NOT a sign that something is wrong.
In cosmology, it is typical to have space infinite in extent, especially for flat or negatively curved space.
In studies of wave propagation, it is typical to consider the far-field, which is done by taking infinite limits. Again, this is not a sign that something has gone wrong.
Once again, I would bet that almost every advanced physics book uses some sort of infinite limit in its calculations.
Imaginary: in our imagination.
I believe referal to infinate is simply a cop put for very many/ very big/ very small. Im talking really here.
And infinite limits seem to me to be an oxymoron.