Use the definition of exp(x) to derive Euler's Formula?

No... e^x is not defined by a summation notation. This is how e is defined,

e = lim_{n→∞} (1+1/n)^n

This is the fundamental definition of e. First appearance in history. All other properties are ultimately derived from this limit.

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No, the limit I gave is the original definition. This is how Jacob Bernoulli defined it when he discovered it back in the 1670's.

How many unique definitions do you think one thing can have in mathematics? Just one! Everything else is a subsequently derived property.

The power series is derived from the fact that dy/dx = y, but that is just one more property. The series expansion is a property, the derivative is a property, so on. The limit is the definition.

Modern mathematicians and teachers use the word "definition" a little too liberally nowadays, when they really mean its an "identity" (requiring a proof).

This is much too long to do in Yahoo! Answers especially without formal math notation but the proofs on Wikipedia are pretty bullet proof.

http://en.wikipedia.org/wiki/Euler%27s_formula#Pro...

yeah, iceman is right, some things are just too tedious to do on yahoo answers.