Calculating time dilation using Euler’s formula

Abstract

This paper shows how the time dilation due to motion, calculated normally using the Lorentz factor, can be encoded in the real part of a complex number by using the Euler's formula. The imaginary part of this complex number will contain the velocity. It also shows how the time dilation due to gravitational attraction can be encoded using the same formula. A combination of time dilation and gravitational time dilation is presented using this formula. The magnitude of this complex number represents the constancy of the speed of light.