well, the first flaw lies in you taking squares.
you have written[math]e^{(i\pi)^{2}}[/math] , when it should be
[math](e^{i\pi})^2[/math]
but then, you might say
[math](e^{i\pi})^{2}=1[/math]
[math](e^{2i\pi})=1[/math]
[math]2i\pi = \ln(1) = 0[/math] and how does that work?
its just like dave said, taking logarithms of complex numbers is a dodgy proposition. Lets just say it is not always true that [math]\ln{e^{z}}=z[/math] if you are working with complex variables.
[edit] why isn't the latex showing up?[/edit]