As already issued here: leanprover-community/mathlib4#15415
It seems that the documentation assumes x.abs to be the polymorphic version, but doesn't see that there is also a different version of abs in the local namespace.
This leads to confusion where one may assume that the absolute value of compex numbers is defined non-standard.
Link for reference: https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Complex/Arg.html#Complex.arg