- #1

- 52

- 4

i was wondering for a while to get a satisfactory proof of the equation : e^i*pi = -1

yes , i know it can be derived from euler's formula ...

which is e^i*x = cosx + isinx ( which can be proved using differential calculus )

so, e^i*pi = cos(pi) + isin(pi) ( which leads to the result we get )

but , the problem is ,i can't seem to get the physical explanation of this equation ( e.g. what e^i*pi = -1 exactly means in reality ) and the process we use to obtain it is extremely abstract( at least it seems to me ) .... is there any proof of this equation which makes a bit more sense ?

my second question is :

how do we evalute the meaning of sini and cosi ?

(suppose if i take x = i then we get ,

e^i*i = cosi + isini

=>e^-1 = cosi + isini

( if i am not wrong this equation can be solved to get individual values for sini and cosi ... but what does a complex angle mean in the first place in ? ) ... i would appreciate answers with proper physical explanation ....

thanks ALL,

THE HARLEQUIN