ABSTRACT
Light is an electromagnetic wave where both the electric and magnetic fields are sinusoidal in terms of both position and time. The simplest mathematical representation of sinusoidal waves is using the trigonometric functions sin and cos. The major advantage of using complex exponential notation for waves is that performing mathematical functions on the waves is much, much easier than dealing with sines and cosines and vast tables of trigonometric identites. When comparing the complex exponential functions representing sinusoidal waves typically used by engineers to those typically used by physicists, there are two subtle differences. Using complex notation, it is fairly straightforward to absorb real part of the phase into the amplitude due to the fact that a sum of phase terms in an exponent is mathematically the same as a product of exponential functions.
