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eiπ Ė1=0

Text Box: The most beautiful equation ever: 
This is the famous Euler's identity   which is considered by many to be the paragon of mathematical beauty.
Three basic arithmetic operations occur: addition, multiplication, and exponentiation. There are also five fundamental mathematical constants:
 
The number 0.
The number 1.
The number π, (π ≈ 3.14159 one definition of π: Ratio circumference of a circle over diameter).
The number e, the base of natural logarithms, (e ≈ 2.71828 definition of 
 
The number i, imaginary unit of the complex numbers. 
Proof:
At first we need to understand how we define the exponentiation with complex exposants .
Obviously it doesnít have any physical meaning like  the exponentiation of real numbers.
One definition we can give to imaginary exponentiation is based on Tailorís development: 
 
Extending the equation to the imaginary numbers, we define
   
                                                                      
 
Whoever is familiar with Taylorís development can easily see that:

Some books give directly the latest formula as definition of the imaginary exponentiation of e.  
Now it is trivial to see that


The real question is if there is a physical meaning behind equations involving imaginary and complex numbers. 
The complex notation can be viewed as a tool for handling two aspects of phenomena such as the amplitude and phase in the case of a sin-wave. The real mystery is the significance of complex in quantum mechanics. (too big subject to develop here). 
There are people saying that this identity is the proof of Godís existence!!! 
In my opinion these statements are the proof that human mind can produce nonsense even from the  beautiful and exact science of Mathematics.