Mrs. S.: I would dearly like to see this proved without recourse to Euler's Equation

Euler's "Identity" ... although Euler didn't actually discover it!

A short proof of this elegant identity combining the most notable math constants (0, 1, i, e and Pi) with math's most basic operations (addition, multiplication and exponentiation) would be a genuine find, I think.

Proof(s) of Euler's Equation (or Theorem) are abundant and the identity above is simply a "special case" with x = Pi, but I was wondering if there was a Silver Bullet Proof, so to speak--probably graphical on the real-imaginary coordinate system.