By "much nicer", I was merely attempting to point out that drblast's formula:

     e^(tau*i/2)+1=0

could be stated as:

     e^(i*tau) = 1

As in the article. Whether that's intrinsically "better" than Euler's Identity is a different question, but not what I was discussing here.

I actually disagree with that logic as well. If you just knew that e^(i * pi) = -1, then how would you know, whether halving that exponent would yield +i or -i?

Considering that, we'd need to state Euler's identity as: e^(i * pi/2) = i, but again we'd know nothing about fractions of that exponent. And there we go!

The point is, Euler's identity is a nice property of the definition of complex numbers, but in itself, not too generic. That's why OP's form, e^(i*tau) = 1, would do just fine.

Edit: fixed asterisks.