Euler's Formula

Hi,

Is there any "intuitive" way to understand Euler's Formula:

e^(ix) = cosx + i sinx

For example, you can visualize or you intiuitvely feel the value
of certain limits tending to something. How does one visualize
e^(ix)? Imagining e^ix, based on what e^x is, is impossible.

Also, I would like know what proof did Euler present for
this formula? Was it the one using infinite series for e^x?
Or it must have been something pretty "complex". :)

(Request: Take it easy with the mathematical jargon in your
reply. I come from a non-mathematical background. I am
an engineer!)

Thanks,
Anand


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