There several things to improve:

• Some functions do not have an error description at all:

  cpython/Doc/c-api/complex.rst

  Lines 106 to 115 in 7e91e0d

  	.. c:function:: PyObject* PyComplex_FromCComplex(Py_complex v)
  	Create a new Python complex number object from a C :c:type:`Py_complex` value.
  	.. c:function:: PyObject* PyComplex_FromDoubles(double real, double imag)
  	Return a new :c:type:`PyComplexObject` object from *real* and *imag*.

  So, we should add that these functions can fail.
• Some functions mention the error case, but do not mention that exception is set:

  cpython/Doc/c-api/complex.rst

  Lines 152 to 153 in 7e91e0d

  	to :meth:`~object.__index__`. Upon failure, this method returns ``-1.0`` as a real
  	value.

Plus, I would unify the wording in some other functions.

Linked PRs

• gh-121834: Improve complex C-API docs #121835
• [3.13] gh-121834: Improve complex C-API docs (GH-121835) #121895
• [3.12] gh-121834: Improve complex C-API docs (GH-121835) #121897