[caylus]

Arguably it makes it more clear what's really going on. With tau, the identity can be formulated either:

- e^(iτ) = 1, meaning that taking a full revolution around the complex plane brings you back to 1, where you started

- e^(iτ/2) = -1, meaning that taking a half revolution takes you to the opposite of where you started, -1.

If you insist on the "contains the additive identity" formulation (which IMO is gratuitous because e^(ix) is all about the complex plane, not regular addition and multiplication), you can do either e^(iτ) + 0 = 1, or e^(iτ) - 1 = 0.

[antonvs]

Good points, I was just thinking about it superficially.