Everyone knows that e^[pi(i)] == -1
Using this we also know that e^[2pi(i)] == 1
What I believe I proved was e^i == 1 using the following proof:
Start with [e^i]
Since raising a number to 1 just gives you the number let's raise this to the equivalent of 1 or [(2pi)/(2pi)]
[e^i]^[(2pi)/(2pi)]
When raising a power to a power you just multiply them to get the new power also when multiplying 2 number you can also pull them apart as follows
i*[(2pi)/(2pi)] == [2pi(i)]*[1/2pi] returning to the original problem we now get
[e^(2pi(i))]^[1/(2pi)] but since we already know that [e^(2pi(i))] == 1 we get the following
[1^(1/{2pi})] but 1 raised to any power equal to 1 therefore we have e^1 eqaul to 1 which we know isn't correct.
Where did I mess up?