Re: How is the 4th Dimension TIME*square root of -1?

The simple answer is the presence of the square root of negative one is 
just a mathematical convenience; and, if you continue studying 
relativity, how imaginary numbers creep into relativity will become 
obvious.  The next level of answer is more technical and may require some 
study of the references cited before it makes sense.

In spacetime, the interval between two events is defined as the sum of 
the squares of the differences of spatial coordinates (x, y, and z) minus 
the square of the difference in time coordinate.  Some authors prefer all 
signs to be positive so that the formula seems merely an extension of the 
more familiar distance formulas for 2 and 3-dimensional space.  To effect 
the later, the negative sign is replaced by the square of 'i' (the square 
root of negative 1).

My preferred reference for the above is pages 10 to 11 of Bernard F. 
Schutz' A First Course in General Relativity.

Thanks for your question.

sid