I feel like the result in both cases should be inf+0j,

What does the IEEE-754 spec say is the correct result?

I'm not sure what the spec itself says--evidently I'd have to pay for it to find out. I don't see any mention of complex numbers on the wikipedia page, so maybe it's not covered: https://en.wikipedia.org/wiki/IEEE_754

For what it's worth, my version of g++ claims to support IEEE-754 for floats, and I get 1.0f / 0.0f = inf, which agrees with numpy behavior in the case of real numbers.

Right, my question is about what g++ does for complex division. The C99 spec seems to say:

if the first operand is a nonzero finite number or an infinity and the second operand is a zero, then the result of the / operator is an infinity.

and

A complex or imaginary value with at least one infinite part is regarded as an infinity
(even if its other part is a NaN)

which suggests that the behavior of 1 / a is correct, and reciprocal diverges from the standard.

The implementation is here:

C99 Annex G.5.1.4: the result from np.reciprocal is wrong, and the result from 1/np.complex_(0) is correct. One should have assert np.isinf(np.reciprocal(0+0j)), but it's not specified which complex infinity is returned (and inf+nanj is an infinity).

There's also something else strange here:

>>> z = np.complex_(0+0j)
>>> 1/z
(inf+nanj)
>>> 1/(1/z)
(nan+nanj)

Python doesn't consider (inf, nan) as an infinity in division:

>>> 1/complex(float("inf"), float("nan"))
(nan+nanj)

so it seems there's deviation from C99 spec also there. (In C99, 1/(1/(0+0*I)) appears to evaluate to zero.)

Ah, that makes sense. Thanks! I can try to make a PR to change reciprocal to match 1 / a this weekend.

Python doesn't consider (inf, nan) as an infinity in division

@pv, now it's a bug: python/cpython#119372. Here is a corresponding NumPy issue: #26560