James Clerk-Maxwell did.
explain your project
electromagnetic
Because they can. There really isn't a "why" involved. If they couldn't, THEN we'd need to explain why.
The concept of light propagation, the transmission of light along an optical fiber, can be described by two theories. According to the first theory, light is described as a simple ray. This theory is the ray theory, or geometrical optics, approach. The advantage of the ray approach is that you get a clearer picture of the propagation of light along a fiber. The ray theory is used to approximate the light acceptance and guiding properties of optical fibers. According to the second theory, light is described as an electromagnetic wave. This theory is the mode theory, or wave representation, approach. The mode theory describes the behavior of light within an optical fiber. The mode theory is useful in describing the optical fiber properties of absorption, attenuation, and dispersion
Many properties of electronmagnetic waves can be explained by a wave model. However, some properties can be explained by a particle model.
The "ether" is a hypothetical substance, postulated in the past to explain the propagation of electromagnetic waves such as light. The word is hardly used nowadays. Empty space takes over this role, but it doesn't have all the properties that were expected of the ether in the past.
explain your project
Complex equations? Do you mean complicated equations whose solution is 17, - or equations with complex (non-real) coefficients or solutions? If you can explain, please resubmit your question.
Electromagnetic (EM) propagation is dual in nature. Early experiments on light and/or electrons to see if they were waves or particles gave puzzling results. Experiments to prove the propagations were waves gave positive results to confirm that they were indeed waves. When other experiments were conducted to prove they were particles the result was that they acted like particles. Someone jestingly suggested that we call them "wavicles". When electromagnetic waves interact with other waves and/or need to have the characteristics of waves, they act like waves. If however the propagating energy interact with particles by non-wave like behavior then it acts as a particle. To explain how electromagnetic energy propagates in a vacuum, why just consider it as particles for that journey. This may not seem as a satisfactory answer, but as A. Einstein once remarked "the Universe is not only stranger than you imagine, it is stranger than you can imagine" When electromagnetic energy acts as a particle they are called "photons". There are separate math equations to deal with EM propagation for waves & as particles. They both work and they both can predict results.
A conclusion.
It means explain how electromagnetic waves are different than water and sound waves.
electromagnetic
electromagnetic
mathematical equations to solve the unsolvable
Because it's fun
You need to explain your question in more detail.
ultraviolet light