This question cropped up while I was playing with the equation for time dilation. If I set the speed to be $i$ (imaginary unit) the answer from the equation still makes sense, but does that matter if the input data doesn't make sense? Or rather does the input data make sense?

Let $v=i$ and $c=2$ then $T' = T \sqrt{1 -\frac{i^2} {2^2}}$, or $T' = T \sqrt{1 -\frac{-1} {4}}$, or $T' = T \sqrt{\frac{5}{4}}$.

Am I completely out of bounds here or is it something that can be explained?