Full Idea
Proponents of complex numbers had ultimately to argue that the new operations shared with the original paradigms a susceptibility to construal in physical terms. The geometrical models of complex numbers answered to this need.
Gist of Idea
The defenders of complex numbers had to show that they could be expressed in physical terms
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5)
Book Reference
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.176
A Reaction
[A nice example of the verbose ideas which this website aims to express in plain English!] The interest is not that they had to be described physically (which may pander to an uninformed audience), but that they could be so described.