I would recommend conforming to the C99 Standard Appendix G.6 for complex arithmetic which differs slightly from the expected results above.

csinh(+∞ + i∞) returns ±∞ + iNaN (where the sign of the real part of the result is
unspecified) and raises the ‘‘invalid’’ floating-point exception
ccosh(+∞ + i∞) returns ±∞ + iNaN (where the sign of the real part of the result is
unspecified) and raises the ‘‘invalid’’ floating-point exception.
ctanh(+∞ + i∞) returns 1 ± i0 (where the sign of the imaginary part of the result is
unspecified).

Likely other special cases may not be handled consistent with the C99 standard either.

Yes, those seem most reasonable. Note that cmplx.IsInf(±∞ + iNaN) is true.

See also cmplx.Sqrt which gives sqrt((+Inf+Infi)) -> (+Inf+NaNi). The C99 standard says, "csqrt(x+i∞) returns +∞+i∞, for all x (including NaN)."

So, yes. Others are not consistent with C99 either.

CC @griesemer

Also cmplx.Pow behaves differently to math.Pow when raising NaN**0.

https://play.golang.org/p/b5zuzP7j7nk

Change https://golang.org/cl/169501 mentions this issue: math/cmplx: handle special cases

Change https://golang.org/cl/206037 mentions this issue: Revert "math/cmplx: handle special cases"

As @ianlancetaylor wrote on the revert:

Reason for revert: The new tests fail at least on s390x and MIPS. This is likely a minor bug in the compiler or runtime. But this point in the release cycle is not the time to debug these details, which are unlikely to be new. Let's try again for 1.15.

Change https://golang.org/cl/220689 mentions this issue: math/cmplx: handle special cases