Began thinking about it last night, follow my logic.
Know that:
If e^i? = -1, then e^? = -1^-i
And that Ln(-x) = Ln(x) + i?
And that the definition of a rational number is a number that can be written in the form a/b where a and b are integers in their most reduced form.

e+? = a/b
e^e+? =e^a/b
e^e*e^? = e^a/b
e^e * (-1)^-i = e^a/b
(e^e * (-1)^-i)^i = (e^a/b)^i
-e^ei = e^ai/b
(-e^ei)^-i = (e^ai/b)^-i
-e^e = e^a/b
(-e^e)^b = (e^a/b)^b
-e^eb = e^a
eb + ?i = a

e + ? = eb + ?i / b
e + ? = eb/b + ?i/b
e + ? = e + ?i/b
? = ?i/b
?b = ?i
b = i

Since i is not an integer, we have a proof by contradiction. Q.E.D