User talk:Omoreira
Nov 11, 2015
Mathematically speaking, yes and here lies the beauty of the Euler's formula (in my opinion) because we can take advantage of the nice exponential function properties, particularly, those pertaining to its derivation / integration and use it to quickly solve analytically many physical and mathematical problems that would otherwise would be challenging and long to solve. Of course, to interpret the solutions and translate to the real and physical, we look at the real part of complex exponential which a periodic function. For instance, in the context of mechanical vibrations problem, the motion of small object attached to an elastic string satisfies a second-order differential equation. We can find that solution is complex-valued (i.e it can be expressed as a complex exponential function), to translate and interpret in terms of real and physical we look at the real part of complex solution and this is a periodic function. Thus, one may find that object will oscillate with increasing or decrease amplitude depending on initial constraints