Incorrect overflows for complex powers when base is infinite

[skirpichev]

Bug report

Bug description:

Consider this, for example:

Python 3.16.0a0 (heads/main:ee68f5f46a1, Aug 12 2026, 11:19:39) [GCC 14.2.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> complex('inf+0j')**1
Traceback (most recent call last):
  File "<python-input-0>", line 1, in <module>
    complex('inf+0j')**1
    ~~~~~~~~~~~~~~~~~^^~
OverflowError: complex exponentiation

c.f. the real case:

>>> float('inf')**1
inf

See also http://stackoverflow.com/q/18243270/270986

The generic algorithm returns a correct answer (match GNU MPC, for example), but sets errno incorrectly:

>>> import _testcapi
>>> _testcapi._py_c_pow(complex('inf'), 1)
((inf+nanj), 34)
>>> from gmpy2 import mpc
>>> mpc('inf')**1
mpc('inf+nanj')

CPython versions tested on:

CPython main branch

Operating systems tested on:

No response

Linked PRs

• gh-156693: correct complex powers with infinite bases #156694