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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

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