Subject: Why does everyone assume that complex times are invalid?

I have a basic understanding of Special Relativity. But I think there is
an unwarranted assumption involved.

If speeds greater than light are used in relativistic equations, the 
time variable, T, works out to be a complex number (i.e., having an 
imaginary component)  I have frequently heard this cited as "proof" that 
speeds greater than that of light are therefore impossible.  I see no 
reason behind this assumption; I have seen engineering calculations made 
regarding actual projects which utilized complex numbers to describe real 
physical quantities.  Just because we do not yet know what interpretation 
to place on a transit time which is an imaginary quantity would not seem to 
mean that it therefore cannot occur.  Is there any sound theoretical basis 
for declaring that complex quantities cannot be used in calculating transit 
times?

Re: Why does everyone assume that complex times are invalid?