Proposed resolution:

This wording is relative to N4296.

1. Change [complex.value.ops] around p9 as indicated

   template<class T> complex<T> polar(const T& rho, const T& theta = 0);
   

   -?- Requires: rho shall be non-negative and non-NaN. theta shall be finite.

   -9- Returns: The complex value corresponding to a complex number whose magnitude is rho and whose phase angle is theta.

[ 2015-02, Cologne ]

Discussion on whether theta should also be constrained.
TK: infinite theta doesn't make sense, whereas infinite rho does (theta is on a compact domain, rho is on a non-compact domain).
AM: We already have a narrow contract, so I don't mind adding further requirements. Any objections to requiring that theta be finite?
Some more discussion, but general consensus. Agreement that if someone finds the restrictions problematic, they should write a proper paper to address how std::polar should behave. For now, we allow infinite rho (but not NaN and not negative), and require finite theta.

No objections to tentatively ready.

Different implementations give different answers for the following code:

#include <iostream>
#include <complex>

int main ()
{
  std::cout << std::polar(-1.0, -1.0) << '\n';
  return 0;
}

One implementation prints:

(nan, nan)

Another:

(-0.243068, 0.243068)

Which is correct? Or neither?

In this list, Howard Hinnant wrote:

I've read this over several times. I've consulted C++11, C11, and IEC 10967-3. [snip]

I'm finding:

1. The magnitude of a complex number == abs(c) == hypot(c.real(), c.imag()) and is always non-negative (by all three of the above standards).

2. Therefore no complex number exists for which abs(c) < 0.

3. Therefore when the first argument to std::polar (which is called rho) is negative, no complex number can be formed which meets the post-conidtion that abs(c) == rho.

One could argue that this is already covered in [complex.numbers]/3, but I think it's worth making explicit.