Oooooo... so close, the i IS positive.
Here is my labored proof of this, which I will mention is the ONLY actual showing of PROOF their function is correct

Euler's Equation

Calculus Proof of Euler's Equation

Series Proof of Euler's Equation
In any case, using pi for x in the equation gives us a value of -1. Therefore, the equation given by Doug31 can be created (except i is positive!).
To answer Fox Tails' question, ln of a negative can potentially exist so long as it can be cancelled by some arithmetic reason, such as in Euler's Formula.
Can I win for most caring to prove himself right?
My thanks to Microsoft Equation Editor 3.0