Wow! Thanks everyone for the thoughtful replies. It seems that the way to 
go is to create an alternative to Complex{T} types in which there is but a 
single ComplexInfinity. This would be an interesting project but I'm not a 
top-notch coder ... perhaps someone would like to take it on. When they do, 
creating polynomial and rational function types that properly handle 
complex infinity would be good too. That way f(x) =(2x-1)/(x+1) would 
evaluate f(Inf) as 2. :-)

On Saturday, January 10, 2015 at 7:55:09 AM UTC-6, Ed Scheinerman wrote:
>
> Is there a way to have a single complex infinity? This may come at the 
> cost of computational efficiency I suppose, but I can think of situations 
> where all of the following give the same result:
>
> julia> (1+1im)/0
> Inf + Inf*im
>
> julia> 1im/0
> NaN + Inf*im
>
> julia> 1/0 + im
> Inf + 1.0im
>
> It would be nice (sometimes) if these were all the same ComplexInf, say. 
> Perhaps there's an "extended complex numbers" module for this sort of work? 
>

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