Euler’s identity e^(iπ)+1 = 0 is a central, rigorously proven result in complex analysis. This note does not dispute its correctness inside that formalism. Instead it isolates a single, widely overlooked modeling choice that arises when the analytic identity is applied to measurable angles in physics and engineering: the implicit treatment of angular measures as if they were plain, unitless real numbers. I (1) explain why the analytic/trigonometric power series force a particular angular normalization (radians); (2) show concretely, via a bradian renormalization and a kilogram counterexample, that the usual "divide-by-1 rad" maneuveris a convention that cannot be elevated to a general principle; (3) formalize the issue as atype/coercion error; and (4) show direct implications for phasor calculus and the Schrodinger plane-wave ansatz. I finish with minimal, implementable prescriptions (explicit coercion or typed wrappers) that preserve numerical results while restoring unit-aware rigor.