But faster than light time becomes imaginary
According to the formula for time dilation, the Lorentz factor
gamma = 1/sqrt(1 - v^2/c^2)
If v > c then we have in the denominator the square root of a negative number, hence gamma is imaginary.
Time won't flow backwards at all, but orthogonally, whatever that might imply.
Is there some reason that we are overlooking this factor?