Lambert function and Wolfram or "±infinity+i×K=±infinity" ?

[Gil]

Are my previous post results pure non-sense?

Could you just try, at random, one of my cases?

I entered each time in Wolfram the values k and z=a+ib, with |a| or |b| or both very large (>1E100000) to find the above outputs formulae j, equal to "+inf±i × f,j(k)".

Thanks in advance.